diff --git a/powershell/ql/lib/semmle/code/powershell/Command.qll b/powershell/ql/lib/semmle/code/powershell/Command.qll
index 73c2df41a7a..908a812c3ac 100644
--- a/powershell/ql/lib/semmle/code/powershell/Command.qll
+++ b/powershell/ql/lib/semmle/code/powershell/Command.qll
@@ -40,3 +40,20 @@ class Cmd extends @command, CmdBase {
 
   Redirection getARedirection() { result = this.getRedirection(_) }
 }
+
+/**
+ * An argument to a command.
+ * 
+ * The argument may be named or positional.
+ */
+class Argument extends Expr {
+  Cmd cmd;
+
+  Argument() { cmd.getArgument(_) = this or cmd.getNamedArgument(_) = this }
+
+  Cmd getCmd() { result = cmd }
+
+  int getIndex() { cmd.getArgument(result) = this }
+
+  string getName() { cmd.getNamedArgument(result) = this }
+}
diff --git a/powershell/ql/lib/semmle/code/powershell/InvokeMemberExpression.qll b/powershell/ql/lib/semmle/code/powershell/InvokeMemberExpression.qll
index 1ff04f78e3a..c337a4f08fa 100644
--- a/powershell/ql/lib/semmle/code/powershell/InvokeMemberExpression.qll
+++ b/powershell/ql/lib/semmle/code/powershell/InvokeMemberExpression.qll
@@ -3,7 +3,7 @@ import powershell
 class InvokeMemberExpr extends @invoke_member_expression, MemberExprBase {
   override SourceLocation getLocation() { invoke_member_expression_location(this, result) }
 
-  Expr getBase() { invoke_member_expression(this, result, _) }
+  Expr getQualifier() { invoke_member_expression(this, result, _) }
 
   CmdElement getMember() { invoke_member_expression(this, _, result) }
 
diff --git a/powershell/ql/lib/semmle/code/powershell/controlflow/CfgNodes.qll b/powershell/ql/lib/semmle/code/powershell/controlflow/CfgNodes.qll
index a4f83847963..a94c43ff057 100644
--- a/powershell/ql/lib/semmle/code/powershell/controlflow/CfgNodes.qll
+++ b/powershell/ql/lib/semmle/code/powershell/controlflow/CfgNodes.qll
@@ -166,6 +166,37 @@ module ExprNodes {
 
     predicate isImplicitWrite() { e.isImplicit() }
   }
+
+  /** A control-flow node that wraps an argument expression. */
+  class ArgumentCfgNode extends ExprCfgNode {
+    override string getAPrimaryQlClass() { result = "ArgumentCfgNode" }
+
+    override Argument e;
+
+    final override Argument getExpr() { result = super.getExpr() }
+  }
+
+  private class InvokeMemberChildMapping extends ExprChildMapping, InvokeMemberExpr {
+    override predicate relevantChild(Ast n) { n = this.getQualifier() or n = this.getAnArgument() }
+  }
+
+  /** A control-flow node that wraps an `InvokeMemberExpr` expression. */
+  class InvokeMemberCfgNode extends ExprCfgNode {
+    override string getAPrimaryQlClass() { result = "InvokeMemberCfgNode" }
+
+    override InvokeMemberChildMapping e;
+
+    final override InvokeMemberExpr getExpr() { result = super.getExpr() }
+
+    final ExprCfgNode getQualifier() { e.hasCfgChild(e.getQualifier(), this, result) }
+  }
+
+    /** A control-flow node that wraps a qualifier expression. */
+  class QualifierCfgNode extends ExprCfgNode {
+    QualifierCfgNode() { this = any(InvokeMemberCfgNode invoke).getQualifier() }
+
+    InvokeMemberCfgNode getInvokeMember() { this = result.getQualifier() }
+  }
 }
 
 module StmtNodes {
diff --git a/powershell/ql/lib/semmle/code/powershell/controlflow/internal/Scope.qll b/powershell/ql/lib/semmle/code/powershell/controlflow/internal/Scope.qll
index 1a23cacec35..84b794dbee8 100644
--- a/powershell/ql/lib/semmle/code/powershell/controlflow/internal/Scope.qll
+++ b/powershell/ql/lib/semmle/code/powershell/controlflow/internal/Scope.qll
@@ -17,4 +17,23 @@ Scope scopeOf(Ast n) {
 class Scope extends Ast, @script_block {
   /** Gets the outer scope, if any. */
   Scope getOuterScope() { result = scopeOf(this) }
+
+  /**
+   * Gets the `i`'th paramter in this scope.
+   *
+   * This may be both function paramters and parameter block parameters.
+   */
+  Parameter getParameter(int i) {
+    exists(Function func |
+      func.getBody() = this and
+      result = func.getParameter(i)
+    )
+  }
+
+  /**
+   * Gets a paramter in this scope.
+   *
+   * This may be both function paramters and parameter block parameters.
+   */
+  Parameter getAParameter() { result = this.getParameter(_) }
 }
diff --git a/powershell/ql/test/library-tests/ast/Expressions/expressions.ql b/powershell/ql/test/library-tests/ast/Expressions/expressions.ql
index 22d68304d1f..6f3064f5c40 100644
--- a/powershell/ql/test/library-tests/ast/Expressions/expressions.ql
+++ b/powershell/ql/test/library-tests/ast/Expressions/expressions.ql
@@ -10,7 +10,7 @@ query predicate cmdExpr(CmdExpr cmd, Expr e) {
 }
 
 query predicate invokeMemoryExpression(InvokeMemberExpr invoke, Expr e, int i, Expr arg) {
-    e = invoke.getBase() and
+    e = invoke.getQualifier() and
     arg = invoke.getArgument(i)
 }
 
diff --git a/powershell/ql/test/library-tests/dataflow/local/test.ps1 b/powershell/ql/test/library-tests/dataflow/local/test.ps1
index 6530b256fdc..86bbd7cadaf 100644
--- a/powershell/ql/test/library-tests/dataflow/local/test.ps1
+++ b/powershell/ql/test/library-tests/dataflow/local/test.ps1
@@ -1,8 +1,8 @@
-$a1 = Source()
-Sink($a1)
+$a1 = Source
+Sink $a1
 
-$b = GetBool()
+$b = GetBool
 if($b) {
-    $a2 = Source()
+    $a2 = Source
 }
-Sink($a2)
\ No newline at end of file
+Sink $a2
\ No newline at end of file