diff --git a/types/jquery/index.d.ts b/types/jquery/index.d.ts
index 024dcc3ab8..b139de1632 100644
--- a/types/jquery/index.d.ts
+++ b/types/jquery/index.d.ts
@@ -37,6 +37,8 @@ declare const $: JQueryStatic;
 
 // Used by JQuery.Event
 type _Event = Event;
+// Used by JQuery.Promise3 and JQuery.Promise
+type _Promise<T> = Promise<T>;
 
 interface JQueryStatic<TElement extends Node = HTMLElement> {
     /**
@@ -6281,7 +6283,7 @@ declare namespace JQuery {
      */
     interface Promise3<TR, TJ, TN,
         UR, UJ, UN,
-        VR, VJ, VN> extends PromiseLike<TR> {
+        VR, VJ, VN> extends _Promise<TR>, PromiseLike<TR> {
         /**
          * Add handlers to be called when the Deferred object is either resolved or rejected.
          *
@@ -6685,9 +6687,9 @@ declare namespace JQuery {
         catch<ARF = never, AJF = never, ANF = never,
             BRF = never, BJF = never, BNF = never,
             CRF = never, CJF = never, CNF = never>
-            (failFilter: (t: TJ, u: UJ, v: VJ) => Promise3<ARF, AJF, ANF,
+            (failFilter?: ((t: TJ, u: UJ, v: VJ) => Promise3<ARF, AJF, ANF,
                 BRF, BJF, BNF,
-                CRF, CJF, CNF> | Thenable<ARF> | ARF): Promise3<ARF, AJF, ANF,
+                CRF, CJF, CNF> | Thenable<ARF> | ARF) | undefined | null): Promise3<ARF, AJF, ANF,
             BRF, BJF, BNF,
             CRF, CJF, CNF>;
     }
@@ -6709,7 +6711,7 @@ declare namespace JQuery {
      *
      * @see {@link http://api.jquery.com/Types/#Promise}
      */
-    interface Promise<TR, TJ = any, TN = any> extends PromiseLike<TR> {
+    interface Promise<TR, TJ = any, TN = any> extends _Promise<TR>, PromiseLike<TR> {
         /**
          * Add handlers to be called when the Deferred object is either resolved or rejected.
          *
diff --git a/types/jquery/jquery-tests.ts b/types/jquery/jquery-tests.ts
index d223be9d5c..81ab91d6a3 100644
--- a/types/jquery/jquery-tests.ts
+++ b/types/jquery/jquery-tests.ts
@@ -6512,6 +6512,8 @@ function _Event() {
 }
 
 function jqXHR() {
+    const p: JQuery.jqXHR = {} as any;
+
     function always() {
         // $ExpectType jqXHR<any>
         $.ajax('/echo/json').always((data_jqXHR, textStatus, jqXHR_errorThrown) => {
@@ -6763,6 +6765,10 @@ function jqXHR() {
             errorThrown;
         });
     }
+
+    function compatibleWithPromise(): Promise<any> {
+        return p;
+    }
 }
 
 function Promise3() {
@@ -7145,6 +7151,15 @@ function Promise3() {
         $.ajax('/echo/json').catch(() => {
             return $.ajax('/echo/json');
         });
+
+        // $ExpectType Promise3<never, never, never, never, never, never, never, never, never>
+        $.ajax('/echo/json').catch(undefined);
+
+        // $ExpectType Promise3<never, never, never, never, never, never, never, never, never>
+        $.ajax('/echo/json').catch(null);
+
+        // $ExpectType Promise3<never, never, never, never, never, never, never, never, never>
+        $.ajax('/echo/json').catch();
     }
 
     // As argument to PromiseLike parameter
@@ -7157,6 +7172,10 @@ function Promise3() {
     async function testAsync(p: JQuery.Promise3<string, {}, {}, {}, {}, {}, {}, {}, {}>): Promise<string> {
         return await p;
     }
+
+    function compatibleWithPromise(): Promise<any> {
+        return p;
+    }
 }
 
 function Promise2(p: JQuery.Promise2<string, Error, number, JQuery, string, boolean>) {
@@ -7292,6 +7311,10 @@ function Promise2(p: JQuery.Promise2<string, Error, number, JQuery, string, bool
     async function testAsync(p: JQuery.Promise2<string, {}, {}, {}, {}, {}>): Promise<string> {
         return await p;
     }
+
+    function compatibleWithPromise(): Promise<any> {
+        return p;
+    }
 }
 
 function _Promise(p: JQuery.Promise<string, Error, number>) {
@@ -7404,4 +7427,8 @@ function _Promise(p: JQuery.Promise<string, Error, number>) {
     async function testAsync(p: JQuery.Promise<string, Error, number>): Promise<string> {
         return await p;
     }
+
+    function compatibleWithPromise(): Promise<any> {
+        return p;
+    }
 }