diff --git a/src/com/google/javascript/jscomp/TypeInference.java b/src/com/google/javascript/jscomp/TypeInference.java
index 1204e9854b0..77021699e3e 100644
--- a/src/com/google/javascript/jscomp/TypeInference.java
+++ b/src/com/google/javascript/jscomp/TypeInference.java
@@ -1636,8 +1636,14 @@ private void updateBind(Node n) {
   }
 
   /**
-   * For functions with function parameters, type inference will set the type of a function literal
-   * argument from the function parameter type.
+   * Performs a limited back-inference on function arguments based on the expected parameter types.
+   *
+   * <p>Currently this only does back-inference in two cases: it infers the type of function literal
+   * arguments and adds inferred properties to inferred object-typed arguments.
+   *
+   * <p>For example: if someone calls `Promise<string>.prototype.then` with `(result) => ...` then
+   * we infer that the type of the arrow function is `function(string): ?`, and inside the arrow
+   * function body we know that `result` is a string.
    */
   private void updateTypeOfArguments(Node n, FunctionType fnType) {
     checkState(NodeUtil.isInvocation(n), n);
@@ -1690,16 +1696,23 @@ private void updateTypeOfArguments(Node n, FunctionType fnType) {
           && iArgumentType.isFunctionType()) {
         FunctionType argFnType = iArgumentType.toMaybeFunctionType();
         JSDocInfo argJsdoc = iArgument.getJSDocInfo();
-        boolean declared = argJsdoc != null && argJsdoc.containsDeclaration();
+        // Treat the parameter & return types of the function as 'declared' if the function has
+        // JSDoc with type annotations, or a parameter has inline JSDoc.
+        // Note that this does not distinguish between cases where all parameters have JSDoc vs
+        // only one parameter has JSDoc.
+        boolean declared =
+            (argJsdoc != null && argJsdoc.containsDeclaration())
+                || NodeUtil.functionHasInlineJsdocs(iArgument);
         iArgument.setJSType(matchFunction(restrictedParameter, argFnType, declared));
       }
     }
   }
 
   /**
-   * Take the current function type, and try to match the expected function
-   * type. This is a form of backwards-inference, like record-type constraint
-   * matching.
+   * Take the current function type, and try to match the expected function type. This is a form of
+   * backwards-inference, like record-type constraint matching.
+   *
+   * @param declared Whether the given function type is user-provided as opposed to inferred
    */
   private FunctionType matchFunction(
       FunctionType expectedType, FunctionType currentType, boolean declared) {
diff --git a/test/com/google/javascript/jscomp/TypeCheckTest.java b/test/com/google/javascript/jscomp/TypeCheckTest.java
index 879b60583ac..b61932b415c 100644
--- a/test/com/google/javascript/jscomp/TypeCheckTest.java
+++ b/test/com/google/javascript/jscomp/TypeCheckTest.java
@@ -7715,13 +7715,50 @@ public void testInferredParam8() {
   }
 
   @Test
-  public void testInferredParam9() {
-    // TODO(b/77731069) This should warn "parameter 1 of f does not match formal parameter"
+  public void testFunctionLiteralParamWithInlineJSDocNotInferred() {
+    testTypes(
+        lines(
+            "/** @param {function(string)} x */",
+            "function f(x) {}",
+            "f(function(/** number */ x) {});"),
+        lines(
+            "actual parameter 1 of f does not match formal parameter",
+            "found   : function(number): undefined",
+            "required: function(string): ?"));
+  }
+
+  @Test
+  public void testFunctionLiteralParamWithInlineJSDocNotInferredWithTwoParams() {
+    testTypes(
+        lines(
+            "/** @param {function(string, number)} x */",
+            "function f(x) {}",
+            "f((/** string */ str, num) => {",
+            // TODO(b/123583824): this should be a type mismatch warning.
+            //    found   : number
+            //    expected: string
+            //  but the JSDoc on `str` blocks inference of `num`.
+            "  const /** string */ newStr = num;",
+            "});"));
+  }
+
+  @Test
+  public void testJSDocOnNoParensArrowFnParameterIsIgnored() {
+    // This case is to document a potential bit of confusion: what happens when writing
+    // inline-like JSDoc on a 'naked' arrow function parameter (no parentheses)
+    // The actual behavior is that the JSDoc does nothing: this is equivalent to writing
+    //   /** number */ function(x) { ...
     testTypes(
         lines(
             "/** @param {function(string)} callback */",
             "function foo(callback) {}",
-            "foo(function(/** number */ x) {});"));
+            // The `/** number */` JSDoc is attached to the entire arrow  function, not the
+            // parameter `x`
+            "foo(/** number */ x =>  { var /** number */ y = x; });"),
+        lines(
+            "initializing variable",
+            "found   : string", // type of "x" is inferred to be string
+            "required: number"));
   }
 
   @Test