diff --git a/wgpu/examples/hello-compute/tests.rs b/wgpu/examples/hello-compute/tests.rs
index f7e9cfd863..fa518a06cb 100644
--- a/wgpu/examples/hello-compute/tests.rs
+++ b/wgpu/examples/hello-compute/tests.rs
@@ -9,7 +9,9 @@ use common::{initialize_test, TestParameters};
 #[test]
 fn test_compute_1() {
     initialize_test(
-        TestParameters::default().specific_failure(None, None, Some("V3D"), true),
+        TestParameters::default()
+            .downlevel_flags(wgpu::DownlevelFlags::COMPUTE_SHADERS)
+            .specific_failure(None, None, Some("V3D"), true),
         |ctx| {
             let input = &[1, 2, 3, 4];
 
@@ -26,7 +28,9 @@ fn test_compute_1() {
 #[test]
 fn test_compute_2() {
     initialize_test(
-        TestParameters::default().specific_failure(None, None, Some("V3D"), true),
+        TestParameters::default()
+            .downlevel_flags(wgpu::DownlevelFlags::COMPUTE_SHADERS)
+            .specific_failure(None, None, Some("V3D"), true),
         |ctx| {
             let input = &[5, 23, 10, 9];
 
@@ -43,7 +47,9 @@ fn test_compute_2() {
 #[test]
 fn test_compute_overflow() {
     initialize_test(
-        TestParameters::default().specific_failure(None, None, Some("V3D"), true),
+        TestParameters::default()
+            .downlevel_flags(wgpu::DownlevelFlags::COMPUTE_SHADERS)
+            .specific_failure(None, None, Some("V3D"), true),
         |ctx| {
             let input = &[77031, 837799, 8400511, 63728127];
             pollster::block_on(assert_execute_gpu(
@@ -59,7 +65,9 @@ fn test_compute_overflow() {
 #[test]
 fn test_multithreaded_compute() {
     initialize_test(
-        TestParameters::default().specific_failure(None, None, Some("V3D"), true),
+        TestParameters::default()
+            .downlevel_flags(wgpu::DownlevelFlags::COMPUTE_SHADERS)
+            .specific_failure(None, None, Some("V3D"), true),
         |ctx| {
             use std::{sync::mpsc, thread, time::Duration};
 
diff --git a/wgpu/tests/clear_texture.rs b/wgpu/tests/clear_texture.rs
index 0a2c9dd152..788a37b12b 100644
--- a/wgpu/tests/clear_texture.rs
+++ b/wgpu/tests/clear_texture.rs
@@ -239,7 +239,12 @@ fn single_texture_clear_test(
     // TODO: Read back and check zeroness?
 }
 
-fn clear_texture_tests(ctx: &TestingContext, formats: &[wgpu::TextureFormat], supports_1d: bool) {
+fn clear_texture_tests(
+    ctx: &TestingContext,
+    formats: &[wgpu::TextureFormat],
+    supports_1d: bool,
+    supports_3d: bool,
+) {
     for &format in formats {
         // 1D texture
         if supports_1d {
@@ -265,29 +270,31 @@ fn clear_texture_tests(ctx: &TestingContext, formats: &[wgpu::TextureFormat], su
             },
             wgpu::TextureDimension::D2,
         );
-        // 2D array texture
-        single_texture_clear_test(
-            ctx,
-            format,
-            wgpu::Extent3d {
-                width: 64,
-                height: 64,
-                depth_or_array_layers: 4,
-            },
-            wgpu::TextureDimension::D2,
-        );
-        // volume texture
-        if format.describe().sample_type != wgt::TextureSampleType::Depth {
+        if supports_3d {
+            // 2D array texture
             single_texture_clear_test(
                 ctx,
                 format,
                 wgpu::Extent3d {
-                    width: 16,
-                    height: 16,
-                    depth_or_array_layers: 16,
+                    width: 64,
+                    height: 64,
+                    depth_or_array_layers: 4,
                 },
-                wgpu::TextureDimension::D3,
+                wgpu::TextureDimension::D2,
             );
+            // volume texture
+            if format.describe().sample_type != wgt::TextureSampleType::Depth {
+                single_texture_clear_test(
+                    ctx,
+                    format,
+                    wgpu::Extent3d {
+                        width: 16,
+                        height: 16,
+                        depth_or_array_layers: 16,
+                    },
+                    wgpu::TextureDimension::D3,
+                );
+            }
         }
     }
 }
@@ -297,8 +304,8 @@ fn clear_texture_2d_uncompressed() {
     initialize_test(
         TestParameters::default().features(wgpu::Features::CLEAR_TEXTURE),
         |ctx| {
-            clear_texture_tests(&ctx, TEXTURE_FORMATS_UNCOMPRESSED, true);
-            clear_texture_tests(&ctx, TEXTURE_FORMATS_DEPTH, false);
+            clear_texture_tests(&ctx, TEXTURE_FORMATS_UNCOMPRESSED, true, true);
+            clear_texture_tests(&ctx, TEXTURE_FORMATS_DEPTH, false, true);
         },
     )
 }
@@ -307,9 +314,10 @@ fn clear_texture_2d_uncompressed() {
 fn clear_texture_2d_bc() {
     initialize_test(
         TestParameters::default()
-            .features(wgpu::Features::CLEAR_TEXTURE | wgpu::Features::TEXTURE_COMPRESSION_BC),
+            .features(wgpu::Features::CLEAR_TEXTURE | wgpu::Features::TEXTURE_COMPRESSION_BC)
+            .specific_failure(Some(wgpu::Backends::GL), None, None, true),
         |ctx| {
-            clear_texture_tests(&ctx, TEXTURE_FORMATS_BC, false);
+            clear_texture_tests(&ctx, TEXTURE_FORMATS_BC, false, true);
         },
     )
 }
@@ -318,9 +326,10 @@ fn clear_texture_2d_bc() {
 fn clear_texture_2d_astc() {
     initialize_test(
         TestParameters::default()
-            .features(wgpu::Features::CLEAR_TEXTURE | wgpu::Features::TEXTURE_COMPRESSION_ASTC_LDR),
+            .features(wgpu::Features::CLEAR_TEXTURE | wgpu::Features::TEXTURE_COMPRESSION_ASTC_LDR)
+            .specific_failure(Some(wgpu::Backends::GL), None, None, true),
         |ctx| {
-            clear_texture_tests(&ctx, TEXTURE_FORMATS_ASTC, false);
+            clear_texture_tests(&ctx, TEXTURE_FORMATS_ASTC, false, true);
         },
     )
 }
@@ -329,9 +338,10 @@ fn clear_texture_2d_astc() {
 fn clear_texture_2d_etc2() {
     initialize_test(
         TestParameters::default()
-            .features(wgpu::Features::CLEAR_TEXTURE | wgpu::Features::TEXTURE_COMPRESSION_ETC2),
+            .features(wgpu::Features::CLEAR_TEXTURE | wgpu::Features::TEXTURE_COMPRESSION_ETC2)
+            .specific_failure(Some(wgpu::Backends::GL), None, None, true),
         |ctx| {
-            clear_texture_tests(&ctx, TEXTURE_FORMATS_ETC2, false);
+            clear_texture_tests(&ctx, TEXTURE_FORMATS_ETC2, false, true);
         },
     )
 }
diff --git a/wgpu/tests/common/mod.rs b/wgpu/tests/common/mod.rs
index b9a9b63507..9e97b47d6b 100644
--- a/wgpu/tests/common/mod.rs
+++ b/wgpu/tests/common/mod.rs
@@ -34,7 +34,10 @@ async fn initialize_device(
 pub struct TestingContext {
     pub adapter: Adapter,
     pub adapter_info: wgt::AdapterInfo,
+    pub adapter_downlevel_capabilities: wgt::DownlevelCapabilities,
     pub device: Device,
+    pub device_features: wgt::Features,
+    pub device_limits: wgt::Limits,
     pub queue: Queue,
 }
 
@@ -156,7 +159,7 @@ pub fn initialize_test(parameters: TestParameters, test_function: impl FnOnce(Te
     ))
     .expect("could not find sutable adapter on the system");
 
-    let required_limits = Limits::downlevel_defaults();
+    let required_limits = Limits::downlevel_webgl2_defaults();
     let adapter_info = adapter.get_info();
     let adapter_lowercase_name = adapter_info.name.to_lowercase();
     let adapter_features = adapter.features();
@@ -197,13 +200,16 @@ pub fn initialize_test(parameters: TestParameters, test_function: impl FnOnce(Te
     let (device, queue) = pollster::block_on(initialize_device(
         &adapter,
         parameters.required_features,
-        required_limits,
+        required_limits.clone(),
     ));
 
     let context = TestingContext {
         adapter,
         adapter_info: adapter_info.clone(),
+        adapter_downlevel_capabilities,
         device,
+        device_features: parameters.required_features,
+        device_limits: required_limits,
         queue,
     };