diff --git a/CHANGELOG.md b/CHANGELOG.md
index 15a80a25b..80b986901 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -26,6 +26,7 @@ This project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.htm
 ### Changed
 
 - Expose raw provable methods of a `ZkProgram` on `zkProgram.rawMethods` https://github.com/o1-labs/o1js/pull/1241
+- Reduce number of constraints needed by `rotate()`, `leftShift()` and, `rightShift()` gadgets https://github.com/o1-labs/o1js/pull/1201
 
 ### Fixed
 
diff --git a/src/bindings b/src/bindings
index 5df84bf1f..cea062267 160000
--- a/src/bindings
+++ b/src/bindings
@@ -1 +1 @@
-Subproject commit 5df84bf1f06c9c1e984e19d067fcf10c8ae53299
+Subproject commit cea062267c2cf81edf50fee8ca9578824c056731
diff --git a/src/lib/gadgets/bitwise.ts b/src/lib/gadgets/bitwise.ts
index d4fc7ff5f..bd4b65f77 100644
--- a/src/lib/gadgets/bitwise.ts
+++ b/src/lib/gadgets/bitwise.ts
@@ -276,8 +276,10 @@ function rot(
   );
   // Compute next row
   rangeCheck64(shifted);
-  // Compute following row
-  rangeCheck64(excess);
+  // note: range-checking `shifted` and `field` is enough.
+  // * excess < 2^rot follows from the bound check and the rotation equation in the gate
+  // * rotated < 2^64 follows from rotated = excess + shifted (because shifted has to be a multiple of 2^rot)
+  // for a proof, see https://github.com/o1-labs/o1js/pull/1201
   return [rotated, excess, shifted];
 }
 
diff --git a/src/lib/gadgets/bitwise.unit-test.ts b/src/lib/gadgets/bitwise.unit-test.ts
index 6fa914a79..73d908af1 100644
--- a/src/lib/gadgets/bitwise.unit-test.ts
+++ b/src/lib/gadgets/bitwise.unit-test.ts
@@ -1,6 +1,6 @@
 import { ZkProgram } from '../proof_system.js';
 import {
-  equivalent,
+  equivalentProvable as equivalent,
   equivalentAsync,
   field,
   fieldWithRng,
@@ -228,7 +228,7 @@ constraintSystem(
   ifNotAllConstant(contains(xorChain(64)))
 );
 
-let rotChain: GateType[] = ['Rot64', 'RangeCheck0', 'RangeCheck0'];
+let rotChain: GateType[] = ['Rot64', 'RangeCheck0'];
 let isJustRotate = ifNotAllConstant(
   and(contains(rotChain), withoutGenerics(equals(rotChain)))
 );
diff --git a/tests/vk-regression/plain-constraint-system.ts b/tests/vk-regression/plain-constraint-system.ts
index 875135e2c..b5d0c1f44 100644
--- a/tests/vk-regression/plain-constraint-system.ts
+++ b/tests/vk-regression/plain-constraint-system.ts
@@ -36,6 +36,7 @@ const GroupCS = constraintSystem('Group Primitive', {
 const BitwiseCS = constraintSystem('Bitwise Primitive', {
   rot() {
     let a = Provable.witness(Field, () => new Field(12));
+    Gadgets.rangeCheck64(a); // `rotate()` doesn't do this
     Gadgets.rotate(a, 2, 'left');
     Gadgets.rotate(a, 2, 'right');
     Gadgets.rotate(a, 4, 'left');
diff --git a/tests/vk-regression/vk-regression.json b/tests/vk-regression/vk-regression.json
index 03974dc49..f60540c9f 100644
--- a/tests/vk-regression/vk-regression.json
+++ b/tests/vk-regression/vk-regression.json
@@ -169,8 +169,8 @@
     "digest": "Bitwise Primitive",
     "methods": {
       "rot": {
-        "rows": 13,
-        "digest": "2c0dadbba96fd7ddb9adb7d643425ce3"
+        "rows": 10,
+        "digest": "c38703de755b10edf77bf24269089274"
       },
       "xor": {
         "rows": 15,
@@ -185,12 +185,12 @@
         "digest": "b12ad7e8a3fd28b765e059357dbe9e44"
       },
       "leftShift": {
-        "rows": 7,
-        "digest": "66de39ad3dd5807f760341ec85a6cc41"
+        "rows": 5,
+        "digest": "451f550bf73fecf53c9be82367572cb8"
       },
       "rightShift": {
-        "rows": 7,
-        "digest": "a32264f2d4c3092f30d600fa9506385b"
+        "rows": 5,
+        "digest": "d0793d4a326d480eaa015902dc34bc39"
       },
       "and": {
         "rows": 19,