diff --git a/src/dawn/native/Toggles.cpp b/src/dawn/native/Toggles.cpp
index 8f229703f1..f9f39a789d 100644
--- a/src/dawn/native/Toggles.cpp
+++ b/src/dawn/native/Toggles.cpp
@@ -142,6 +142,14 @@ namespace dawn::native {
              {"disable_snorm_read",
               "Disables reading from Snorm textures which is unsupported on some platforms.",
               "https://crbug.com/dawn/667"}},
+            {Toggle::DisableDepthRead,
+             {"disable_depth_read",
+              "Disables reading from depth textures which is unsupported on some platforms.",
+              "https://crbug.com/dawn/667"}},
+            {Toggle::DisableStencilRead,
+             {"disable_stencil_read",
+              "Disables reading from stencil textures which is unsupported on some platforms.",
+              "https://crbug.com/dawn/667"}},
             {Toggle::DisableDepthStencilRead,
              {"disable_depth_stencil_read",
               "Disables reading from depth/stencil textures which is unsupported on some "
diff --git a/src/dawn/native/Toggles.h b/src/dawn/native/Toggles.h
index 0b47221d51..d9748fb45a 100644
--- a/src/dawn/native/Toggles.h
+++ b/src/dawn/native/Toggles.h
@@ -44,6 +44,8 @@ namespace dawn::native {
         DisableBaseInstance,
         DisableIndexedDrawBuffers,
         DisableSnormRead,
+        DisableDepthRead,
+        DisableStencilRead,
         DisableDepthStencilRead,
         DisableBGRARead,
         DisableSampleVariables,
diff --git a/src/dawn/native/opengl/DeviceGL.cpp b/src/dawn/native/opengl/DeviceGL.cpp
index 3d95b1b663..c520ab1c25 100644
--- a/src/dawn/native/opengl/DeviceGL.cpp
+++ b/src/dawn/native/opengl/DeviceGL.cpp
@@ -71,6 +71,12 @@ namespace dawn::native::opengl {
         bool supportsSnormRead =
             gl.IsAtLeastGL(4, 4) || gl.IsGLExtensionSupported("GL_EXT_render_snorm");
 
+        bool supportsDepthRead =
+            gl.IsAtLeastGL(3, 0) || gl.IsGLExtensionSupported("GL_NV_read_depth");
+
+        bool supportsStencilRead =
+            gl.IsAtLeastGL(3, 0) || gl.IsGLExtensionSupported("GL_NV_read_stencil");
+
         bool supportsDepthStencilRead =
             gl.IsAtLeastGL(3, 0) || gl.IsGLExtensionSupported("GL_NV_read_depth_stencil");
 
@@ -100,6 +106,8 @@ namespace dawn::native::opengl {
         SetToggle(Toggle::DisableBaseInstance, !supportsBaseInstance);
         SetToggle(Toggle::DisableIndexedDrawBuffers, !supportsIndexedDrawBuffers);
         SetToggle(Toggle::DisableSnormRead, !supportsSnormRead);
+        SetToggle(Toggle::DisableDepthRead, !supportsDepthRead);
+        SetToggle(Toggle::DisableStencilRead, !supportsStencilRead);
         SetToggle(Toggle::DisableDepthStencilRead, !supportsDepthStencilRead);
         SetToggle(Toggle::DisableBGRARead, !supportsBGRARead);
         SetToggle(Toggle::DisableSampleVariables, !supportsSampleVariables);
diff --git a/src/dawn/tests/end2end/NonzeroTextureCreationTests.cpp b/src/dawn/tests/end2end/NonzeroTextureCreationTests.cpp
index 365b150e1d..2b98552765 100644
--- a/src/dawn/tests/end2end/NonzeroTextureCreationTests.cpp
+++ b/src/dawn/tests/end2end/NonzeroTextureCreationTests.cpp
@@ -108,11 +108,22 @@ namespace {
                                   GetParam().mMipCount > 1 &&
                                   HasToggleEnabled("disable_r8_rg8_mipmaps"));
 
-            // TODO(crbug.com/dawn/667): Work around the fact that some platforms do not support
-            // reading from depth/stencil.
+            // TODO(crbug.com/dawn/667): ANGLE claims to support NV_read_stencil, but won't read
+            // correctly from a DEPTH32F_STENCIL8 texture.
             DAWN_SUPPRESS_TEST_IF(GetParam().mFormat == wgpu::TextureFormat::Depth24PlusStencil8 &&
                                   GetParam().mAspect == wgpu::TextureAspect::StencilOnly &&
-                                  HasToggleEnabled("disable_depth_stencil_read"));
+                                  IsANGLE());
+
+            // TODO(crbug.com/dawn/667): Work around the fact that some platforms do not support
+            // reading depth.
+            DAWN_TEST_UNSUPPORTED_IF(GetParam().mAspect == wgpu::TextureAspect::DepthOnly &&
+                                     HasToggleEnabled("disable_depth_read"));
+
+            // TODO(crbug.com/dawn/667): Work around the fact that some platforms do not support
+            // reading stencil.
+            DAWN_TEST_UNSUPPORTED_IF(GetParam().mAspect == wgpu::TextureAspect::StencilOnly &&
+                                     HasToggleEnabled("disable_stencil_read"));
+
             // GL may support the feature, but reading data back is not implemented.
             DAWN_TEST_UNSUPPORTED_IF(GetParam().mFormat == wgpu::TextureFormat::BC1RGBAUnorm &&
                                      (IsOpenGL() || IsOpenGLES()));
@@ -362,7 +373,7 @@ DAWN_INSTANTIATE_TEST_P(NonzeroDepthTextureCreationTests,
                          VulkanBackend({"nonzero_clear_resources_on_creation_for_testing"},
                                        {"lazy_clear_resource_on_first_use"})},
                         {wgpu::TextureFormat::Depth32Float},
-                        {wgpu::TextureAspect::All},
+                        {wgpu::TextureAspect::DepthOnly},
                         {wgpu::TextureUsage(wgpu::TextureUsage::RenderAttachment |
                                             wgpu::TextureUsage::CopySrc),
                          wgpu::TextureUsage::CopySrc},