diff --git a/cpp/ql/src/semmle/code/cpp/ir/dataflow/DefaultTaintTracking.qll b/cpp/ql/src/semmle/code/cpp/ir/dataflow/DefaultTaintTracking.qll
index fea47e1b5bd..aa5cfbe1fab 100644
--- a/cpp/ql/src/semmle/code/cpp/ir/dataflow/DefaultTaintTracking.qll
+++ b/cpp/ql/src/semmle/code/cpp/ir/dataflow/DefaultTaintTracking.qll
@@ -21,6 +21,40 @@ private predicate predictableInstruction(Instruction instr) {
   predictableInstruction(instr.(UnaryInstruction).getUnary())
 }
 
+/**
+ * Functions that we should only allow taint to flow through (to the return
+ * value) if all but the source argument are 'predictable'.  This is done to
+ * emulate the old security library's implementation rather than due to any
+ * strong belief that this is the right approach.
+ *
+ * Note that the list itself is not very principled; it consists of all the
+ * functions listed in the old security library's [default] `isPureFunction`
+ * that have more than one argument, but are not in the old taint tracking
+ * library's `returnArgument` predicate.  In addition, `strlen` is included
+ * because it's also a special case in flow to return values.
+ */
+predicate predictableOnlyFlow(string name) {
+  name = "strcasestr" or
+  name = "strchnul" or
+  name = "strchr" or
+  name = "strchrnul" or
+  name = "strcmp" or
+  name = "strcspn" or
+  name = "strlen" or // special case
+  name = "strncmp" or
+  name = "strndup" or
+  name = "strnlen" or
+  name = "strrchr" or
+  name = "strspn" or
+  name = "strstr" or
+  name = "strtod" or
+  name = "strtof" or
+  name = "strtol" or
+  name = "strtoll" or
+  name = "strtoq" or
+  name = "strtoul"
+}
+
 private DataFlow::Node getNodeForSource(Expr source) {
   isUserInput(source, _) and
   (
@@ -123,15 +157,16 @@ private predicate nodeIsBarrier(DataFlow::Node node) {
 
 private predicate instructionTaintStep(Instruction i1, Instruction i2) {
   // Expressions computed from tainted data are also tainted
-  i2 =
-    any(CallInstruction call |
-      isPureFunction(call.getStaticCallTarget().getName()) and
-      call.getAnArgument() = i1 and
-      forall(Instruction arg | arg = call.getAnArgument() | arg = i1 or predictableInstruction(arg)) and
-      // flow through `strlen` tends to cause dubious results, if the length is
-      // bounded.
-      not call.getStaticCallTarget().getName() = "strlen"
-    )
+  exists(CallInstruction call, int argIndex | call = i2 |
+    isPureFunction(call.getStaticCallTarget().getName()) and
+    i1 = getACallArgumentOrIndirection(call, argIndex) and
+    forall(Instruction arg | arg = call.getAnArgument() |
+      arg = getACallArgumentOrIndirection(call, argIndex) or predictableInstruction(arg)
+    ) and
+    // flow through `strlen` tends to cause dubious results, if the length is
+    // bounded.
+    not call.getStaticCallTarget().getName() = "strlen"
+  )
   or
   // Flow through pointer dereference
   i2.(LoadInstruction).getSourceAddress() = i1
@@ -172,7 +207,8 @@ private predicate instructionTaintStep(Instruction i1, Instruction i2) {
     any(CallInstruction call |
       exists(int indexIn |
         modelTaintToReturnValue(call.getStaticCallTarget(), indexIn) and
-        i1 = getACallArgumentOrIndirection(call, indexIn)
+        i1 = getACallArgumentOrIndirection(call, indexIn) and
+        not predictableOnlyFlow(call.getStaticCallTarget().getName())
       )
     )
   or
diff --git a/cpp/ql/test/library-tests/dataflow/security-taint/tainted_diff.expected b/cpp/ql/test/library-tests/dataflow/security-taint/tainted_diff.expected
index bd82e48f8c6..ed954b5444a 100644
--- a/cpp/ql/test/library-tests/dataflow/security-taint/tainted_diff.expected
+++ b/cpp/ql/test/library-tests/dataflow/security-taint/tainted_diff.expected
@@ -1,15 +1,8 @@
-| test.cpp:38:23:38:28 | call to getenv | test.cpp:40:6:40:33 | ! ... | IR only |
-| test.cpp:38:23:38:28 | call to getenv | test.cpp:40:7:40:12 | call to strcmp | IR only |
-| test.cpp:38:23:38:28 | call to getenv | test.cpp:40:7:40:33 | (bool)... | IR only |
 | test.cpp:49:23:49:28 | call to getenv | test.cpp:50:15:50:24 | envStr_ptr | AST only |
 | test.cpp:49:23:49:28 | call to getenv | test.cpp:50:28:50:40 | & ... | AST only |
 | test.cpp:49:23:49:28 | call to getenv | test.cpp:50:29:50:40 | envStrGlobal | AST only |
 | test.cpp:49:23:49:28 | call to getenv | test.cpp:52:2:52:12 | * ... | AST only |
 | test.cpp:49:23:49:28 | call to getenv | test.cpp:52:3:52:12 | envStr_ptr | AST only |
-| test.cpp:60:29:60:34 | call to getenv | test.cpp:64:10:64:14 | bytes | IR only |
-| test.cpp:60:29:60:34 | call to getenv | test.cpp:64:18:64:23 | call to strlen | IR only |
-| test.cpp:60:29:60:34 | call to getenv | test.cpp:64:18:64:37 | (int)... | IR only |
-| test.cpp:60:29:60:34 | call to getenv | test.cpp:64:18:64:37 | ... + ... | IR only |
 | test.cpp:68:28:68:33 | call to getenv | test.cpp:11:20:11:21 | s1 | AST only |
 | test.cpp:68:28:68:33 | call to getenv | test.cpp:67:7:67:13 | copying | AST only |
 | test.cpp:68:28:68:33 | call to getenv | test.cpp:69:10:69:13 | copy | AST only |
diff --git a/cpp/ql/test/library-tests/dataflow/security-taint/tainted_ir.expected b/cpp/ql/test/library-tests/dataflow/security-taint/tainted_ir.expected
index 216d583d925..114c213ff54 100644
--- a/cpp/ql/test/library-tests/dataflow/security-taint/tainted_ir.expected
+++ b/cpp/ql/test/library-tests/dataflow/security-taint/tainted_ir.expected
@@ -14,9 +14,6 @@
 | test.cpp:38:23:38:28 | call to getenv | test.cpp:38:14:38:19 | envStr |  |
 | test.cpp:38:23:38:28 | call to getenv | test.cpp:38:23:38:28 | call to getenv |  |
 | test.cpp:38:23:38:28 | call to getenv | test.cpp:38:23:38:40 | (const char *)... |  |
-| test.cpp:38:23:38:28 | call to getenv | test.cpp:40:6:40:33 | ! ... |  |
-| test.cpp:38:23:38:28 | call to getenv | test.cpp:40:7:40:12 | call to strcmp |  |
-| test.cpp:38:23:38:28 | call to getenv | test.cpp:40:7:40:33 | (bool)... |  |
 | test.cpp:38:23:38:28 | call to getenv | test.cpp:40:14:40:19 | envStr |  |
 | test.cpp:49:23:49:28 | call to getenv | test.cpp:8:24:8:25 | s1 |  |
 | test.cpp:49:23:49:28 | call to getenv | test.cpp:45:13:45:24 | envStrGlobal |  |
@@ -32,10 +29,6 @@
 | test.cpp:60:29:60:34 | call to getenv | test.cpp:60:18:60:25 | userName |  |
 | test.cpp:60:29:60:34 | call to getenv | test.cpp:60:29:60:34 | call to getenv |  |
 | test.cpp:60:29:60:34 | call to getenv | test.cpp:60:29:60:47 | (const char *)... |  |
-| test.cpp:60:29:60:34 | call to getenv | test.cpp:64:10:64:14 | bytes |  |
-| test.cpp:60:29:60:34 | call to getenv | test.cpp:64:18:64:23 | call to strlen |  |
-| test.cpp:60:29:60:34 | call to getenv | test.cpp:64:18:64:37 | (int)... |  |
-| test.cpp:60:29:60:34 | call to getenv | test.cpp:64:18:64:37 | ... + ... |  |
 | test.cpp:60:29:60:34 | call to getenv | test.cpp:64:25:64:32 | userName |  |
 | test.cpp:68:28:68:33 | call to getenv | test.cpp:11:36:11:37 | s2 |  |
 | test.cpp:68:28:68:33 | call to getenv | test.cpp:68:17:68:24 | userName |  |
diff --git a/cpp/ql/test/query-tests/Security/CWE/CWE-807/semmle/TaintedCondition/test.cpp b/cpp/ql/test/query-tests/Security/CWE/CWE-807/semmle/TaintedCondition/test.cpp
index fb6fffb1c44..0430d861095 100644
--- a/cpp/ql/test/query-tests/Security/CWE/CWE-807/semmle/TaintedCondition/test.cpp
+++ b/cpp/ql/test/query-tests/Security/CWE/CWE-807/semmle/TaintedCondition/test.cpp
@@ -35,7 +35,7 @@ void processRequest()
         adminPrivileges = 0; // OK, since it's a 0 and not a 1
      }
 
-     // BAD, but it requires pointer analysis to catch
+     // BAD (requires pointer analysis to catch)
      const char** userp = &currentUser;
      *userp = userName;
      if (!strcmp(currentUser, "admin")) {