diff --git a/src/webgpu/compat/api/validation/encoding/programmable/pipeline_bind_group_compat.spec.ts b/src/webgpu/compat/api/validation/encoding/programmable/pipeline_bind_group_compat.spec.ts
index f9dbcbdc6a09..28c5899577cc 100644
--- a/src/webgpu/compat/api/validation/encoding/programmable/pipeline_bind_group_compat.spec.ts
+++ b/src/webgpu/compat/api/validation/encoding/programmable/pipeline_bind_group_compat.spec.ts
@@ -4,6 +4,7 @@ Tests limitations of bind group usage in a pipeline in compat mode.
 
 import { makeTestGroup } from '../../../../../../common/framework/test_group.js';
 import { keysOf } from '../../../../../../common/util/data_tables.js';
+import { MaxLimitsTestMixin } from '../../../../../gpu_test.js';
 import { kRenderEncodeTypes } from '../../../../../util/command_buffer_maker.js';
 import { CompatibilityTest } from '../../../../compatibility_test.js';
 
@@ -293,7 +294,7 @@ function createResourcesForComputePassTest(
   return { texture, pipeline };
 }
 
-export const g = makeTestGroup(CompatibilityTest);
+export const g = makeTestGroup(MaxLimitsTestMixin(CompatibilityTest));
 
 g.test('twoDifferentTextureViews,render_pass,used')
   .desc(
@@ -329,6 +330,13 @@ Tests that you can not use 2 different views of the same texture in a render pas
   )
   .fn(t => {
     const { encoderType, bindCase, useCase, textureType } = t.params;
+
+    t.skipIf(
+      t.isCompatibility &&
+        textureType === 'storage' &&
+        !(t.device.limits.maxStorageBuffersInFragmentStage! > 2)
+    );
+
     const { bindConfig, fn } = kBindCases[bindCase];
     const { texture, pipeline } = createResourcesForRenderPassTest(t, textureType, bindConfig);
     const { encoder, validateFinish } = t.createEncoder(encoderType);
@@ -347,6 +355,13 @@ Tests that binding 2 different views of the same texture but not using them does
   .params(u => u.combine('encoderType', kRenderEncodeTypes).combine('textureType', kTextureTypes))
   .fn(t => {
     const { encoderType, textureType } = t.params;
+
+    t.skipIf(
+      t.isCompatibility &&
+        textureType === 'storage' &&
+        !(t.device.limits.maxStorageBuffersInFragmentStage! > 2)
+    );
+
     const { texture, pipeline } = createResourcesForRenderPassTest(
       t,
       textureType,