diff --git a/powershell/ql/lib/semmle/code/powershell/InvokeMemberExpression.qll b/powershell/ql/lib/semmle/code/powershell/InvokeMemberExpression.qll
index c337a4f08fa..12017cd7de5 100644
--- a/powershell/ql/lib/semmle/code/powershell/InvokeMemberExpression.qll
+++ b/powershell/ql/lib/semmle/code/powershell/InvokeMemberExpression.qll
@@ -5,11 +5,15 @@ class InvokeMemberExpr extends @invoke_member_expression, MemberExprBase {
 
   Expr getQualifier() { invoke_member_expression(this, result, _) }
 
+  string getName() { result = this.getMember().(StringConstExpr).getValue().getValue() }
+
   CmdElement getMember() { invoke_member_expression(this, _, result) }
 
   Expr getArgument(int i) { invoke_member_expression_argument(this, i, result) }
 
   Expr getAnArgument() { invoke_member_expression_argument(this, _, result) }
 
-  override string toString() { result = "call to " + this.getMember() }
+  override string toString() { result = "call to " + this.getName() }
+
+  override predicate isStatic() { this.getQualifier() instanceof TypeNameExpr }
 }
diff --git a/powershell/ql/lib/semmle/code/powershell/MemberExpr.qll b/powershell/ql/lib/semmle/code/powershell/MemberExpr.qll
index 74cf36b2c53..5af9eef345c 100644
--- a/powershell/ql/lib/semmle/code/powershell/MemberExpr.qll
+++ b/powershell/ql/lib/semmle/code/powershell/MemberExpr.qll
@@ -12,7 +12,7 @@ class MemberExpr extends @member_expression, MemberExprBase {
 
   predicate isNullConditional() { member_expression(this, _, _, true, _) }
 
-  predicate isStatic() { member_expression(this, _, _, _, true) }
+  override predicate isStatic() { member_expression(this, _, _, _, true) }
 
   final override string toString() { result = this.getMember().toString() }
 }
diff --git a/powershell/ql/lib/semmle/code/powershell/MemberExpressionBase.qll b/powershell/ql/lib/semmle/code/powershell/MemberExpressionBase.qll
index 774cbd9b88a..81db24f0019 100644
--- a/powershell/ql/lib/semmle/code/powershell/MemberExpressionBase.qll
+++ b/powershell/ql/lib/semmle/code/powershell/MemberExpressionBase.qll
@@ -1,3 +1,5 @@
 import powershell
 
-class MemberExprBase extends @member_expression_base, Expr { }
+class MemberExprBase extends @member_expression_base, Expr {
+  predicate isStatic() { none() }
+}
diff --git a/powershell/ql/lib/semmle/code/powershell/controlflow/CfgNodes.qll b/powershell/ql/lib/semmle/code/powershell/controlflow/CfgNodes.qll
index 29eaf301998..4ab9bd18661 100644
--- a/powershell/ql/lib/semmle/code/powershell/controlflow/CfgNodes.qll
+++ b/powershell/ql/lib/semmle/code/powershell/controlflow/CfgNodes.qll
@@ -128,6 +128,8 @@ abstract private class NonExprChildMapping extends ChildMapping {
 abstract private class AbstractCallCfgNode extends AstCfgNode {
   override string getAPrimaryQlClass() { result = "CfgCall" }
 
+  abstract string getName();
+
   ExprCfgNode getQualifier() { none() }
 
   abstract ExprCfgNode getArgument(int i);
@@ -137,6 +139,8 @@ abstract private class AbstractCallCfgNode extends AstCfgNode {
   abstract ExprCfgNode getNamedArgument(string name);
 
   abstract ExprCfgNode getAnArgument();
+
+  abstract ExprCfgNode getCommand();
 }
 
 final class CallCfgNode = AbstractCallCfgNode;
@@ -221,6 +225,10 @@ module ExprNodes {
     final override ExprCfgNode getNamedArgument(string name) { none() }
 
     final override ExprCfgNode getAnArgument() { e.hasCfgChild(e.getAnArgument(), this, result) }
+
+    final override string getName() { none() }
+
+    final override ExprCfgNode getCommand() { none() }
   }
 
   /** A control-flow node that wraps a qualifier expression. */
@@ -308,7 +316,9 @@ module StmtNodes {
 
     override ExprCfgNode getAnArgument() { s.hasCfgChild(s.getAnArgument(), this, result) }
 
-    ExprCfgNode getCommand() { s.hasCfgChild(s.getCommand(), this, result) }
+    final override ExprCfgNode getCommand() { s.hasCfgChild(s.getCommand(), this, result) }
+
+    final override string getName() { result = s.getCmdName().getValue().getValue() }
   }
 
   private class AssignStmtChildMapping extends NonExprChildMapping, AssignStmt {