diff --git a/src/compiler/checker.ts b/src/compiler/checker.ts
index fa44b6a3f5b..7d7c9cb89d6 100644
--- a/src/compiler/checker.ts
+++ b/src/compiler/checker.ts
@@ -17863,9 +17863,9 @@ namespace ts {
             if (node.questionToken && isBindingPattern(node.name) && (func as FunctionLikeDeclaration).body) {
                 error(node, Diagnostics.A_binding_pattern_parameter_cannot_be_optional_in_an_implementation_signature);
             }
-            if ((<Identifier>node.name).text === "this") {
+            if (node.name && ((node.name as Identifier).text === "this" || (node.name as Identifier).text === "new")) {
                 if (indexOf(func.parameters, node) !== 0) {
-                    error(node, Diagnostics.A_this_parameter_must_be_the_first_parameter);
+                    error(node, Diagnostics.A_0_parameter_must_be_the_first_parameter, (node.name as Identifier).text as string);
                 }
                 if (func.kind === SyntaxKind.Constructor || func.kind === SyntaxKind.ConstructSignature || func.kind === SyntaxKind.ConstructorType) {
                     error(node, Diagnostics.A_constructor_cannot_have_a_this_parameter);
@@ -19370,14 +19370,6 @@ namespace ts {
             }
         }
 
-        function checkJSDocFunctionType(node: JSDocFunctionType) {
-            for (const p of node.parameters) {
-                // don't bother with normal parameter checking since jsdoc function parameters only consist of a type
-                checkSourceElement(p.type);
-            }
-            checkSourceElement(node.type);
-        }
-
         function checkFunctionOrMethodDeclaration(node: FunctionDeclaration | MethodDeclaration): void {
             checkJSDoc(node);
             checkDecorators(node);
@@ -19923,6 +19915,11 @@ namespace ts {
         function checkVariableLikeDeclaration(node: VariableLikeDeclaration) {
             checkDecorators(node);
             checkSourceElement(node.type);
+
+            // JSDoc `function(string, string): string` syntax results in parameters with no name
+            if (!node.name) {
+                return;
+            }
             // For a computed property, just check the initializer and exit
             // Do not use hasDynamicName here, because that returns false for well known symbols.
             // We want to perform checkComputedPropertyName for all computed properties, including
@@ -22042,7 +22039,7 @@ namespace ts {
                 case SyntaxKind.JSDocParameterTag:
                     return checkSourceElement((node as JSDocParameterTag).typeExpression);
                 case SyntaxKind.JSDocFunctionType:
-                    checkJSDocFunctionType(node as JSDocFunctionType);
+                    checkSignatureDeclaration(node as JSDocFunctionType);
                     // falls through
                 case SyntaxKind.JSDocVariadicType:
                 case SyntaxKind.JSDocNonNullableType:
diff --git a/src/compiler/diagnosticMessages.json b/src/compiler/diagnosticMessages.json
index 9881d32d775..7cd6108576c 100644
--- a/src/compiler/diagnosticMessages.json
+++ b/src/compiler/diagnosticMessages.json
@@ -2064,7 +2064,7 @@
         "category": "Error",
         "code": 2679
     },
-    "A 'this' parameter must be the first parameter.": {
+    "A '{0}' parameter must be the first parameter.": {
         "category": "Error",
         "code": 2680
     },
diff --git a/src/compiler/types.ts b/src/compiler/types.ts
index 85e859603d7..c10cc299728 100644
--- a/src/compiler/types.ts
+++ b/src/compiler/types.ts
@@ -441,7 +441,7 @@ namespace ts {
         // we guarantee that users won't have to pay the price of walking the tree if a dynamic import isn't used.
         /* @internal */
         PossiblyContainsDynamicImport = 1 << 19,
-        JSDoc =          1 << 20, // If node was parsed inside jsdoc
+        JSDoc =              1 << 20, // If node was parsed inside jsdoc
 
         BlockScoped = Let | Const,
 
diff --git a/src/compiler/utilities.ts b/src/compiler/utilities.ts
index dcfad8e776e..3a4ece29f75 100644
--- a/src/compiler/utilities.ts
+++ b/src/compiler/utilities.ts
@@ -4873,6 +4873,7 @@ namespace ts {
             case SyntaxKind.ConstructSignature:
             case SyntaxKind.IndexSignature:
             case SyntaxKind.FunctionType:
+            case SyntaxKind.JSDocFunctionType:
             case SyntaxKind.ConstructorType:
                 return true;
         }
diff --git a/tests/cases/fourslash/codeFixChangeJSDocSyntax1.ts b/tests/cases/fourslash/codeFixChangeJSDocSyntax1.ts
deleted file mode 100644
index 93107ef669b..00000000000
--- a/tests/cases/fourslash/codeFixChangeJSDocSyntax1.ts
+++ /dev/null
@@ -1,4 +0,0 @@
-/// <reference path='fourslash.ts' />
-//// var x: [|?|] = 12;
-
-verify.rangeAfterCodeFix("any");