diff --git a/cpp/ql/lib/semmle/code/cpp/dataflow/ExternalFlow.qll b/cpp/ql/lib/semmle/code/cpp/dataflow/ExternalFlow.qll
index b71a46f6961..69e32d23ec1 100644
--- a/cpp/ql/lib/semmle/code/cpp/dataflow/ExternalFlow.qll
+++ b/cpp/ql/lib/semmle/code/cpp/dataflow/ExternalFlow.qll
@@ -15,16 +15,17 @@
  * reading.
  * 1. The `namespace` column selects a namespace.
  * 2. The `type` column selects a type within that namespace. This column can
- *    introduce template names that can be mentioned in the `signature` column.
+ *    introduce template type names that can be mentioned in the `signature` column.
  *    For example, `vector<T,Allocator>` introduces the template names `T` and
- *    `Allocator`.
+ *    `Allocator`. Non-type template parameters cannot be specified.
  * 3. The `subtypes` is a boolean that indicates whether to jump to an
  *    arbitrary subtype of that type. Set this to `false` if leaving the `type`
  *    blank (for example, a free function).
  * 4. The `name` column optionally selects a specific named member of the type.
- *    Like the `type` column, this column can introduce template names that can
- *    be mentioned in the `signature` column. For example, `insert<InputIt>`
- *    introduces the template name `InputIt`.
+ *    Like the `type` column, this column can introduce template type names
+ *    that can be mentioned in the `signature` column. For example,
+ *    `insert<InputIt>` introduces the template name `InputIt`. Non-type
+ *    template parameters cannot be specified.
  * 5. The `signature` column optionally restricts the named member. If
  *    `signature` is blank then no such filtering is done. The format of the
  *    signature is a comma-separated list of types enclosed in parentheses. The
@@ -633,6 +634,28 @@ string getParameterTypeWithoutTemplateArguments(Function f, int n, boolean canon
   canonical = true
 }
 
+/**
+ * Gets the largest index of a template parameter of `templateFunction` that
+ * is a type template parameter.
+ */
+private int getLastTypeTemplateFunctionParameterIndex(Function templateFunction) {
+  result =
+    max(int index | templateFunction.getTemplateArgument(index) instanceof TypeTemplateParameter)
+}
+
+/** Gets the number of supported template parameters for `templateFunction`. */
+private int getNumberOfSupportedFunctionTemplateArguments(Function templateFunction) {
+  result = count(int i | exists(getSupportedFunctionTemplateArgument(templateFunction, i)) | i)
+}
+
+/** Gets the `i`'th supported template parameter for `templateFunction`. */
+private Locatable getSupportedFunctionTemplateArgument(Function templateFunction, int i) {
+  result = templateFunction.getTemplateArgument(i) and
+  // We don't yet support non-type template parameters in the middle of a
+  // template parameter list
+  i <= getLastTypeTemplateFunctionParameterIndex(templateFunction)
+}
+
 /**
  * Normalize the `n`'th parameter of `f` by replacing template names
  * with `func:N` (where `N` is the index of the template).
@@ -640,18 +663,41 @@ string getParameterTypeWithoutTemplateArguments(Function f, int n, boolean canon
 private string getTypeNameWithoutFunctionTemplates(Function f, int n, int remaining) {
   exists(Function templateFunction |
     templateFunction = getFullyTemplatedFunction(f) and
-    remaining = templateFunction.getNumberOfTemplateArguments() and
+    remaining = getNumberOfSupportedFunctionTemplateArguments(templateFunction) and
     result = getParameterTypeWithoutTemplateArguments(templateFunction, n, _)
   )
   or
   exists(string mid, TypeTemplateParameter tp, Function templateFunction |
     mid = getTypeNameWithoutFunctionTemplates(f, n, remaining + 1) and
     templateFunction = getFullyTemplatedFunction(f) and
-    tp = templateFunction.getTemplateArgument(remaining) and
+    tp = getSupportedFunctionTemplateArgument(templateFunction, remaining)
+  |
     result = mid.replaceAll(tp.getName(), "func:" + remaining.toString())
   )
 }
 
+/**
+ * Gets the largest index of a template parameter of `templateClass` that
+ * is a type template parameter.
+ */
+private int getLastTypeTemplateClassParameterIndex(Class templateClass) {
+  result =
+    max(int index | templateClass.getTemplateArgument(index) instanceof TypeTemplateParameter)
+}
+
+/** Gets the `i`'th supported template parameter for `templateClass`. */
+private Locatable getSupportedClassTemplateArgument(Class templateClass, int i) {
+  result = templateClass.getTemplateArgument(i) and
+  // We don't yet support non-type template parameters in the middle of a
+  // template parameter list
+  i <= getLastTypeTemplateClassParameterIndex(templateClass)
+}
+
+/** Gets the number of supported template parameters for `templateClass`. */
+private int getNumberOfSupportedClassTemplateArguments(Class templateClass) {
+  result = count(int i | exists(getSupportedClassTemplateArgument(templateClass, i)) | i)
+}
+
 /**
  * Normalize the `n`'th parameter of `f` by replacing template names
  * with `class:N` (where `N` is the index of the template).
@@ -661,7 +707,7 @@ private string getTypeNameWithoutClassTemplates(Function f, int n, int remaining
   // If there is a declaring type then we start by expanding the function templates
   exists(Class template |
     isClassConstructedFrom(f.getDeclaringType(), template) and
-    remaining = template.getNumberOfTemplateArguments() and
+    remaining = getNumberOfSupportedClassTemplateArguments(template) and
     result = getTypeNameWithoutFunctionTemplates(f, n, 0)
   )
   or
@@ -673,7 +719,8 @@ private string getTypeNameWithoutClassTemplates(Function f, int n, int remaining
   exists(string mid, TypeTemplateParameter tp, Class template |
     mid = getTypeNameWithoutClassTemplates(f, n, remaining + 1) and
     isClassConstructedFrom(f.getDeclaringType(), template) and
-    tp = template.getTemplateArgument(remaining) and
+    tp = getSupportedClassTemplateArgument(template, remaining)
+  |
     result = mid.replaceAll(tp.getName(), "class:" + remaining.toString())
   )
 }
diff --git a/cpp/ql/test/library-tests/dataflow/external-models/flow.expected b/cpp/ql/test/library-tests/dataflow/external-models/flow.expected
index b1f984680ad..d47ae8950fb 100644
--- a/cpp/ql/test/library-tests/dataflow/external-models/flow.expected
+++ b/cpp/ql/test/library-tests/dataflow/external-models/flow.expected
@@ -30,13 +30,14 @@ models
 | 29 | Summary: ; ; false; RtlMoveMemory; ; ; Argument[*@1]; Argument[*@0]; value; manual |
 | 30 | Summary: ; ; false; RtlMoveVolatileMemory; ; ; Argument[*@1]; Argument[*@0]; value; manual |
 | 31 | Summary: ; ; false; callWithArgument; ; ; Argument[1]; Argument[0].Parameter[0]; value; manual |
-| 32 | Summary: ; ; false; pthread_create; ; ; Argument[@3]; Argument[2].Parameter[@0]; value; manual |
-| 33 | Summary: ; ; false; ymlStepGenerated; ; ; Argument[0]; ReturnValue; taint; df-generated |
-| 34 | Summary: ; ; false; ymlStepManual; ; ; Argument[0]; ReturnValue; taint; manual |
-| 35 | Summary: ; ; false; ymlStepManual_with_body; ; ; Argument[0]; ReturnValue; taint; manual |
-| 36 | Summary: boost::asio; ; false; buffer; ; ; Argument[*0]; ReturnValue; taint; manual |
+| 32 | Summary: ; ; false; callWithNonTypeTemplate<T>; (const T &); ; Argument[*0]; ReturnValue; value; manual |
+| 33 | Summary: ; ; false; pthread_create; ; ; Argument[@3]; Argument[2].Parameter[@0]; value; manual |
+| 34 | Summary: ; ; false; ymlStepGenerated; ; ; Argument[0]; ReturnValue; taint; df-generated |
+| 35 | Summary: ; ; false; ymlStepManual; ; ; Argument[0]; ReturnValue; taint; manual |
+| 36 | Summary: ; ; false; ymlStepManual_with_body; ; ; Argument[0]; ReturnValue; taint; manual |
+| 37 | Summary: boost::asio; ; false; buffer; ; ; Argument[*0]; ReturnValue; taint; manual |
 edges
-| asio_streams.cpp:56:18:56:23 | [summary param] *0 in buffer | asio_streams.cpp:56:18:56:23 | [summary] to write: ReturnValue in buffer | provenance | MaD:36 |
+| asio_streams.cpp:56:18:56:23 | [summary param] *0 in buffer | asio_streams.cpp:56:18:56:23 | [summary] to write: ReturnValue in buffer | provenance | MaD:37 |
 | asio_streams.cpp:87:34:87:44 | read_until output argument | asio_streams.cpp:91:7:91:17 | recv_buffer | provenance | Src:MaD:17  |
 | asio_streams.cpp:87:34:87:44 | read_until output argument | asio_streams.cpp:93:29:93:39 | *recv_buffer | provenance | Src:MaD:17 Sink:MaD:2 |
 | asio_streams.cpp:97:37:97:44 | call to source | asio_streams.cpp:98:7:98:14 | send_str | provenance | TaintFunction |
@@ -45,10 +46,10 @@ edges
 | asio_streams.cpp:100:44:100:62 | call to buffer | asio_streams.cpp:101:7:101:17 | send_buffer | provenance |  |
 | asio_streams.cpp:100:44:100:62 | call to buffer | asio_streams.cpp:103:29:103:39 | *send_buffer | provenance | Sink:MaD:2 |
 | asio_streams.cpp:100:64:100:71 | *send_str | asio_streams.cpp:56:18:56:23 | [summary param] *0 in buffer | provenance |  |
-| asio_streams.cpp:100:64:100:71 | *send_str | asio_streams.cpp:100:44:100:62 | call to buffer | provenance | MaD:36 |
-| test.cpp:4:5:4:17 | [summary param] 0 in ymlStepManual | test.cpp:4:5:4:17 | [summary] to write: ReturnValue in ymlStepManual | provenance | MaD:34 |
-| test.cpp:5:5:5:20 | [summary param] 0 in ymlStepGenerated | test.cpp:5:5:5:20 | [summary] to write: ReturnValue in ymlStepGenerated | provenance | MaD:33 |
-| test.cpp:6:5:6:27 | [summary param] 0 in ymlStepManual_with_body | test.cpp:6:5:6:27 | [summary] to write: ReturnValue in ymlStepManual_with_body | provenance | MaD:35 |
+| asio_streams.cpp:100:64:100:71 | *send_str | asio_streams.cpp:100:44:100:62 | call to buffer | provenance | MaD:37 |
+| test.cpp:4:5:4:17 | [summary param] 0 in ymlStepManual | test.cpp:4:5:4:17 | [summary] to write: ReturnValue in ymlStepManual | provenance | MaD:35 |
+| test.cpp:5:5:5:20 | [summary param] 0 in ymlStepGenerated | test.cpp:5:5:5:20 | [summary] to write: ReturnValue in ymlStepGenerated | provenance | MaD:34 |
+| test.cpp:6:5:6:27 | [summary param] 0 in ymlStepManual_with_body | test.cpp:6:5:6:27 | [summary] to write: ReturnValue in ymlStepManual_with_body | provenance | MaD:36 |
 | test.cpp:7:47:7:52 | value2 | test.cpp:7:64:7:69 | value2 | provenance |  |
 | test.cpp:7:64:7:69 | value2 | test.cpp:7:5:7:30 | *ymlStepGenerated_with_body | provenance |  |
 | test.cpp:10:10:10:18 | call to ymlSource | test.cpp:10:10:10:18 | call to ymlSource | provenance | Src:MaD:16  |
@@ -60,15 +61,15 @@ edges
 | test.cpp:17:10:17:22 | call to ymlStepManual | test.cpp:17:10:17:22 | call to ymlStepManual | provenance |  |
 | test.cpp:17:10:17:22 | call to ymlStepManual | test.cpp:18:10:18:10 | y | provenance | Sink:MaD:1 |
 | test.cpp:17:24:17:24 | x | test.cpp:4:5:4:17 | [summary param] 0 in ymlStepManual | provenance |  |
-| test.cpp:17:24:17:24 | x | test.cpp:17:10:17:22 | call to ymlStepManual | provenance | MaD:34 |
+| test.cpp:17:24:17:24 | x | test.cpp:17:10:17:22 | call to ymlStepManual | provenance | MaD:35 |
 | test.cpp:21:10:21:25 | call to ymlStepGenerated | test.cpp:21:10:21:25 | call to ymlStepGenerated | provenance |  |
 | test.cpp:21:10:21:25 | call to ymlStepGenerated | test.cpp:22:10:22:10 | z | provenance | Sink:MaD:1 |
 | test.cpp:21:27:21:27 | x | test.cpp:5:5:5:20 | [summary param] 0 in ymlStepGenerated | provenance |  |
-| test.cpp:21:27:21:27 | x | test.cpp:21:10:21:25 | call to ymlStepGenerated | provenance | MaD:33 |
+| test.cpp:21:27:21:27 | x | test.cpp:21:10:21:25 | call to ymlStepGenerated | provenance | MaD:34 |
 | test.cpp:25:11:25:33 | call to ymlStepManual_with_body | test.cpp:25:11:25:33 | call to ymlStepManual_with_body | provenance |  |
 | test.cpp:25:11:25:33 | call to ymlStepManual_with_body | test.cpp:26:10:26:11 | y2 | provenance | Sink:MaD:1 |
 | test.cpp:25:35:25:35 | x | test.cpp:6:5:6:27 | [summary param] 0 in ymlStepManual_with_body | provenance |  |
-| test.cpp:25:35:25:35 | x | test.cpp:25:11:25:33 | call to ymlStepManual_with_body | provenance | MaD:35 |
+| test.cpp:25:35:25:35 | x | test.cpp:25:11:25:33 | call to ymlStepManual_with_body | provenance | MaD:36 |
 | test.cpp:32:11:32:36 | call to ymlStepGenerated_with_body | test.cpp:32:11:32:36 | call to ymlStepGenerated_with_body | provenance |  |
 | test.cpp:32:11:32:36 | call to ymlStepGenerated_with_body | test.cpp:33:10:33:11 | z2 | provenance | Sink:MaD:1 |
 | test.cpp:32:41:32:41 | x | test.cpp:7:47:7:52 | value2 | provenance |  |
@@ -76,7 +77,7 @@ edges
 | test.cpp:46:30:46:32 | *arg [x] | test.cpp:47:12:47:19 | *arg [x] | provenance |  |
 | test.cpp:47:12:47:19 | *arg [x] | test.cpp:48:13:48:13 | *s [x] | provenance |  |
 | test.cpp:48:13:48:13 | *s [x] | test.cpp:48:16:48:16 | x | provenance | Sink:MaD:1 |
-| test.cpp:52:5:52:18 | [summary param] *3 in pthread_create [x] | test.cpp:52:5:52:18 | [summary] to write: Argument[2].Parameter[*0] in pthread_create [x] | provenance | MaD:32 |
+| test.cpp:52:5:52:18 | [summary param] *3 in pthread_create [x] | test.cpp:52:5:52:18 | [summary] to write: Argument[2].Parameter[*0] in pthread_create [x] | provenance | MaD:33 |
 | test.cpp:52:5:52:18 | [summary] to write: Argument[2].Parameter[*0] in pthread_create [x] | test.cpp:46:30:46:32 | *arg [x] | provenance |  |
 | test.cpp:56:2:56:2 | *s [post update] [x] | test.cpp:59:55:59:64 | *& ... [x] | provenance |  |
 | test.cpp:56:2:56:18 | ... = ... | test.cpp:56:2:56:2 | *s [post update] [x] | provenance |  |
@@ -103,6 +104,13 @@ edges
 | test.cpp:101:26:101:26 | x | test.cpp:63:6:63:21 | [summary param] 1 in callWithArgument | provenance |  |
 | test.cpp:103:63:103:63 | x | test.cpp:63:6:63:21 | [summary param] 1 in callWithArgument | provenance |  |
 | test.cpp:104:62:104:62 | x | test.cpp:63:6:63:21 | [summary param] 1 in callWithArgument | provenance |  |
+| test.cpp:111:3:111:25 | [summary param] *0 in callWithNonTypeTemplate | test.cpp:111:3:111:25 | [summary] to write: ReturnValue in callWithNonTypeTemplate | provenance | MaD:32 |
+| test.cpp:114:10:114:18 | call to ymlSource | test.cpp:114:10:114:18 | call to ymlSource | provenance | Src:MaD:16  |
+| test.cpp:114:10:114:18 | call to ymlSource | test.cpp:118:44:118:44 | *x | provenance |  |
+| test.cpp:118:11:118:42 | call to callWithNonTypeTemplate | test.cpp:118:11:118:42 | call to callWithNonTypeTemplate | provenance |  |
+| test.cpp:118:11:118:42 | call to callWithNonTypeTemplate | test.cpp:119:10:119:11 | y2 | provenance | Sink:MaD:1 |
+| test.cpp:118:44:118:44 | *x | test.cpp:111:3:111:25 | [summary param] *0 in callWithNonTypeTemplate | provenance |  |
+| test.cpp:118:44:118:44 | *x | test.cpp:118:11:118:42 | call to callWithNonTypeTemplate | provenance | MaD:32 |
 | windows.cpp:17:8:17:25 | [summary param] *0 in CommandLineToArgvA | windows.cpp:17:8:17:25 | [summary] to write: ReturnValue[**] in CommandLineToArgvA | provenance | MaD:18 |
 | windows.cpp:22:15:22:29 | *call to GetCommandLineA | windows.cpp:22:15:22:29 | *call to GetCommandLineA | provenance | Src:MaD:3  |
 | windows.cpp:22:15:22:29 | *call to GetCommandLineA | windows.cpp:24:8:24:11 | * ... | provenance |  |
@@ -314,6 +322,14 @@ nodes
 | test.cpp:101:26:101:26 | x | semmle.label | x |
 | test.cpp:103:63:103:63 | x | semmle.label | x |
 | test.cpp:104:62:104:62 | x | semmle.label | x |
+| test.cpp:111:3:111:25 | [summary param] *0 in callWithNonTypeTemplate | semmle.label | [summary param] *0 in callWithNonTypeTemplate |
+| test.cpp:111:3:111:25 | [summary] to write: ReturnValue in callWithNonTypeTemplate | semmle.label | [summary] to write: ReturnValue in callWithNonTypeTemplate |
+| test.cpp:114:10:114:18 | call to ymlSource | semmle.label | call to ymlSource |
+| test.cpp:114:10:114:18 | call to ymlSource | semmle.label | call to ymlSource |
+| test.cpp:118:11:118:42 | call to callWithNonTypeTemplate | semmle.label | call to callWithNonTypeTemplate |
+| test.cpp:118:11:118:42 | call to callWithNonTypeTemplate | semmle.label | call to callWithNonTypeTemplate |
+| test.cpp:118:44:118:44 | *x | semmle.label | *x |
+| test.cpp:119:10:119:11 | y2 | semmle.label | y2 |
 | windows.cpp:17:8:17:25 | [summary param] *0 in CommandLineToArgvA | semmle.label | [summary param] *0 in CommandLineToArgvA |
 | windows.cpp:17:8:17:25 | [summary] to write: ReturnValue[**] in CommandLineToArgvA | semmle.label | [summary] to write: ReturnValue[**] in CommandLineToArgvA |
 | windows.cpp:22:15:22:29 | *call to GetCommandLineA | semmle.label | *call to GetCommandLineA |
@@ -472,6 +488,7 @@ subpaths
 | test.cpp:21:27:21:27 | x | test.cpp:5:5:5:20 | [summary param] 0 in ymlStepGenerated | test.cpp:5:5:5:20 | [summary] to write: ReturnValue in ymlStepGenerated | test.cpp:21:10:21:25 | call to ymlStepGenerated |
 | test.cpp:25:35:25:35 | x | test.cpp:6:5:6:27 | [summary param] 0 in ymlStepManual_with_body | test.cpp:6:5:6:27 | [summary] to write: ReturnValue in ymlStepManual_with_body | test.cpp:25:11:25:33 | call to ymlStepManual_with_body |
 | test.cpp:32:41:32:41 | x | test.cpp:7:47:7:52 | value2 | test.cpp:7:5:7:30 | *ymlStepGenerated_with_body | test.cpp:32:11:32:36 | call to ymlStepGenerated_with_body |
+| test.cpp:118:44:118:44 | *x | test.cpp:111:3:111:25 | [summary param] *0 in callWithNonTypeTemplate | test.cpp:111:3:111:25 | [summary] to write: ReturnValue in callWithNonTypeTemplate | test.cpp:118:11:118:42 | call to callWithNonTypeTemplate |
 | windows.cpp:27:36:27:38 | *cmd | windows.cpp:17:8:17:25 | [summary param] *0 in CommandLineToArgvA | windows.cpp:17:8:17:25 | [summary] to write: ReturnValue[**] in CommandLineToArgvA | windows.cpp:27:17:27:34 | **call to CommandLineToArgvA |
 | windows.cpp:537:40:537:41 | *& ... | windows.cpp:473:17:473:37 | [summary param] *1 in RtlCopyVolatileMemory | windows.cpp:473:17:473:37 | [summary param] *0 in RtlCopyVolatileMemory [Return] | windows.cpp:537:27:537:37 | RtlCopyVolatileMemory output argument |
 | windows.cpp:542:38:542:39 | *& ... | windows.cpp:479:17:479:35 | [summary param] *1 in RtlCopyDeviceMemory | windows.cpp:479:17:479:35 | [summary param] *0 in RtlCopyDeviceMemory [Return] | windows.cpp:542:25:542:35 | RtlCopyDeviceMemory output argument |
diff --git a/cpp/ql/test/library-tests/dataflow/external-models/flow.ext.yml b/cpp/ql/test/library-tests/dataflow/external-models/flow.ext.yml
index f0df3e749e6..8e200aabfbd 100644
--- a/cpp/ql/test/library-tests/dataflow/external-models/flow.ext.yml
+++ b/cpp/ql/test/library-tests/dataflow/external-models/flow.ext.yml
@@ -17,4 +17,5 @@ extensions:
       - ["", "", False, "ymlStepGenerated", "", "", "Argument[0]", "ReturnValue", "taint", "df-generated"]
       - ["", "", False, "ymlStepManual_with_body", "", "", "Argument[0]", "ReturnValue", "taint", "manual"]
       - ["", "", False, "ymlStepGenerated_with_body", "", "", "Argument[0]", "ReturnValue", "taint", "df-generated"]
-      - ["", "", False, "callWithArgument", "", "", "Argument[1]", "Argument[0].Parameter[0]", "value", "manual"]
\ No newline at end of file
+      - ["", "", False, "callWithArgument", "", "", "Argument[1]", "Argument[0].Parameter[0]", "value", "manual"]
+      - ["", "", False, "callWithNonTypeTemplate<T>", "(const T &)", "", "Argument[*0]", "ReturnValue", "value", "manual"]
\ No newline at end of file
diff --git a/cpp/ql/test/library-tests/dataflow/external-models/sinks.expected b/cpp/ql/test/library-tests/dataflow/external-models/sinks.expected
index 0cc01c8165e..e28349b7159 100644
--- a/cpp/ql/test/library-tests/dataflow/external-models/sinks.expected
+++ b/cpp/ql/test/library-tests/dataflow/external-models/sinks.expected
@@ -13,3 +13,5 @@
 | test.cpp:75:11:75:11 | y | test-sink |
 | test.cpp:83:11:83:11 | y | test-sink |
 | test.cpp:89:11:89:11 | y | test-sink |
+| test.cpp:116:10:116:11 | y1 | test-sink |
+| test.cpp:119:10:119:11 | y2 | test-sink |
diff --git a/cpp/ql/test/library-tests/dataflow/external-models/sources.expected b/cpp/ql/test/library-tests/dataflow/external-models/sources.expected
index 401fffdbd59..cb7e06b801d 100644
--- a/cpp/ql/test/library-tests/dataflow/external-models/sources.expected
+++ b/cpp/ql/test/library-tests/dataflow/external-models/sources.expected
@@ -2,6 +2,7 @@
 | test.cpp:10:10:10:18 | call to ymlSource | local |
 | test.cpp:56:8:56:16 | call to ymlSource | local |
 | test.cpp:94:10:94:18 | call to ymlSource | local |
+| test.cpp:114:10:114:18 | call to ymlSource | local |
 | windows.cpp:22:15:22:29 | *call to GetCommandLineA | local |
 | windows.cpp:34:17:34:38 | *call to GetEnvironmentStringsA | local |
 | windows.cpp:39:36:39:38 | GetEnvironmentVariableA output argument | local |
diff --git a/cpp/ql/test/library-tests/dataflow/external-models/test.cpp b/cpp/ql/test/library-tests/dataflow/external-models/test.cpp
index f357b934b2f..af11ff958f5 100644
--- a/cpp/ql/test/library-tests/dataflow/external-models/test.cpp
+++ b/cpp/ql/test/library-tests/dataflow/external-models/test.cpp
@@ -102,4 +102,19 @@ void test_callWithArgument() {
 	}
 	callWithArgument(StructWithOperatorCall_has_constructor_2(), x);
 	callWithArgument(StructWithOperatorCall_no_constructor_2(), x);
-}
\ No newline at end of file
+}
+
+template<int N, typename T>
+T callWithNonTypeTemplate(const T&);
+
+template<typename T, int N>
+T callWithNonTypeTemplate(const T&);
+
+void test_callWithNonTypeTemplate() {
+	int x = ymlSource();
+	int y1 = callWithNonTypeTemplate<10, int>(x);
+	ymlSink(y1); // $ MISSING: ir
+
+	int y2 = callWithNonTypeTemplate<int, 10>(x);
+	ymlSink(y2); // $ ir
+}
diff --git a/cpp/ql/test/library-tests/dataflow/taint-tests/test_mad-signatures.expected b/cpp/ql/test/library-tests/dataflow/taint-tests/test_mad-signatures.expected
index 2409e711e6d..e0002aa9c03 100644
--- a/cpp/ql/test/library-tests/dataflow/taint-tests/test_mad-signatures.expected
+++ b/cpp/ql/test/library-tests/dataflow/taint-tests/test_mad-signatures.expected
@@ -26843,6 +26843,24 @@ getParameterTypeName
 | atl.cpp:71:5:71:17 | _U_STRINGorID | 0 | unsigned int |
 | atl.cpp:72:5:72:17 | _U_STRINGorID | 0 | LPCTSTR |
 | atl.cpp:72:5:72:17 | _U_STRINGorID | 0 | const char * |
+| atl.cpp:96:5:96:10 | CA2AEX | 0 | LPCSTR |
+| atl.cpp:96:5:96:10 | CA2AEX | 0 | const char * |
+| atl.cpp:96:5:96:10 | CA2AEX | 1 | UINT |
+| atl.cpp:96:5:96:10 | CA2AEX | 1 | unsigned int |
+| atl.cpp:97:5:97:10 | CA2AEX | 0 | LPCSTR |
+| atl.cpp:97:5:97:10 | CA2AEX | 0 | const char * |
+| atl.cpp:124:5:124:11 | CA2CAEX | 0 | LPCSTR |
+| atl.cpp:124:5:124:11 | CA2CAEX | 0 | const char * |
+| atl.cpp:124:5:124:11 | CA2CAEX | 1 | UINT |
+| atl.cpp:124:5:124:11 | CA2CAEX | 1 | unsigned int |
+| atl.cpp:125:5:125:11 | CA2CAEX | 0 | LPCSTR |
+| atl.cpp:125:5:125:11 | CA2CAEX | 0 | const char * |
+| atl.cpp:149:5:149:10 | CA2WEX | 0 | LPCSTR |
+| atl.cpp:149:5:149:10 | CA2WEX | 0 | const char * |
+| atl.cpp:149:5:149:10 | CA2WEX | 1 | UINT |
+| atl.cpp:149:5:149:10 | CA2WEX | 1 | unsigned int |
+| atl.cpp:150:5:150:10 | CA2WEX | 0 | LPCSTR |
+| atl.cpp:150:5:150:10 | CA2WEX | 0 | const char * |
 | atl.cpp:196:12:196:14 | Add | 0 | INARGTYPclass:0 |
 | atl.cpp:198:12:198:17 | Append | 0 | const CAtlArray & |
 | atl.cpp:199:10:199:13 | Copy | 0 | const CAtlArray & |
@@ -27083,6 +27101,10 @@ getParameterTypeName
 | atl.cpp:940:10:940:18 | SetString | 0 | PCXSTR |
 | atl.cpp:940:10:940:18 | SetString | 0 | const class:0 * |
 | atl.cpp:942:11:942:20 | operator[] | 0 | int |
+| atl.cpp:1018:10:1018:10 | operator= | 0 | MakeOther && |
+| atl.cpp:1018:10:1018:10 | operator= | 0 | const MakeOther & |
+| atl.cpp:1023:10:1023:10 | operator= | 0 | MakeOther && |
+| atl.cpp:1023:10:1023:10 | operator= | 0 | const MakeOther & |
 | atl.cpp:1036:5:1036:12 | CStringT | 0 | const VARIANT & |
 | atl.cpp:1036:5:1036:12 | CStringT | 0 | const tagVARIANT & |
 | atl.cpp:1037:5:1037:12 | CStringT | 0 | const VARIANT & |
@@ -27286,6 +27308,8 @@ getParameterTypeName
 | standalone_iterators.cpp:20:7:20:7 | operator= | 0 | const int_iterator_by_trait & |
 | standalone_iterators.cpp:20:7:20:7 | operator= | 0 | int_iterator_by_trait && |
 | standalone_iterators.cpp:23:27:23:36 | operator++ | 0 | int |
+| standalone_iterators.cpp:28:13:28:13 | operator= | 0 | const iterator_traits & |
+| standalone_iterators.cpp:28:13:28:13 | operator= | 0 | iterator_traits && |
 | standalone_iterators.cpp:36:7:36:7 | operator= | 0 | const non_iterator & |
 | standalone_iterators.cpp:36:7:36:7 | operator= | 0 | non_iterator && |
 | standalone_iterators.cpp:39:18:39:27 | operator++ | 0 | int |
@@ -27297,6 +27321,8 @@ getParameterTypeName
 | standalone_iterators.cpp:66:30:66:39 | operator++ | 0 | int |
 | standalone_iterators.cpp:68:30:68:39 | operator-- | 0 | int |
 | standalone_iterators.cpp:70:31:70:39 | operator= | 0 | int |
+| standalone_iterators.cpp:74:13:74:13 | operator= | 0 | const iterator_traits & |
+| standalone_iterators.cpp:74:13:74:13 | operator= | 0 | iterator_traits && |
 | standalone_iterators.cpp:82:7:82:7 | container | 0 | const container & |
 | standalone_iterators.cpp:82:7:82:7 | container | 0 | container && |
 | standalone_iterators.cpp:82:7:82:7 | operator= | 0 | const container & |