diff --git a/GPU/Vulkan/FramebufferVulkan.cpp b/GPU/Vulkan/FramebufferVulkan.cpp
index 5cf7ab2cbd..d6124cc467 100644
--- a/GPU/Vulkan/FramebufferVulkan.cpp
+++ b/GPU/Vulkan/FramebufferVulkan.cpp
@@ -434,13 +434,15 @@ void FramebufferManagerVulkan::BlitFramebufferDepth(VirtualFramebuffer *src, Vir
 	bool matchingDepthBuffer = src->z_address == dst->z_address && src->z_stride != 0 && dst->z_stride != 0;
 	bool matchingSize = src->width == dst->width && src->height == dst->height;
 	bool matchingRenderSize = src->renderWidth == dst->renderWidth && src->renderHeight == dst->renderHeight;
-
-	if (gstate_c.Supports(GPU_SUPPORTS_ANY_COPY_IMAGE) && matchingDepthBuffer && matchingRenderSize && matchingSize) {
+	if (matchingDepthBuffer && matchingRenderSize && matchingSize) {
+		// TODO: Currently, this copies depth AND stencil, which is a problem.  See #9740.
 		draw_->CopyFramebufferImage(src->fbo, 0, 0, 0, 0, dst->fbo, 0, 0, 0, 0, src->renderWidth, src->renderHeight, 1, Draw::FB_DEPTH_BIT);
 	} else if (matchingDepthBuffer && matchingSize) {
+		/*
 		int w = std::min(src->renderWidth, dst->renderWidth);
 		int h = std::min(src->renderHeight, dst->renderHeight);
 		draw_->BlitFramebuffer(src->fbo, 0, 0, w, h, dst->fbo, 0, 0, w, h, Draw::FB_DEPTH_BIT, Draw::FB_BLIT_NEAREST);
+		*/
 	}
 }
 
diff --git a/ext/native/thin3d/thin3d.h b/ext/native/thin3d/thin3d.h
index fdb68a3849..6b3a6dfac9 100644
--- a/ext/native/thin3d/thin3d.h
+++ b/ext/native/thin3d/thin3d.h
@@ -555,6 +555,8 @@ struct DeviceCaps {
 	bool logicOpSupported;
 	bool framebufferCopySupported;
 	bool framebufferBlitSupported;
+	bool framebufferDepthCopySupported;
+	bool framebufferDepthBlitSupported;
 };
 
 struct TextureDesc {
diff --git a/ext/native/thin3d/thin3d_d3d11.cpp b/ext/native/thin3d/thin3d_d3d11.cpp
index e7ca762369..a40d4c4bfc 100644
--- a/ext/native/thin3d/thin3d_d3d11.cpp
+++ b/ext/native/thin3d/thin3d_d3d11.cpp
@@ -217,6 +217,9 @@ D3D11DrawContext::D3D11DrawContext(ID3D11Device *device, ID3D11DeviceContext *de
 
 	caps_.depthRangeMinusOneToOne = false;
 	caps_.framebufferBlitSupported = false;
+	caps_.framebufferCopySupported = true;
+	caps_.framebufferDepthBlitSupported = false;
+	caps_.framebufferDepthCopySupported = true;
 
 	D3D11_FEATURE_DATA_D3D11_OPTIONS options{};
 	HRESULT result = device_->CheckFeatureSupport(D3D11_FEATURE_D3D11_OPTIONS, &options, sizeof(options));
diff --git a/ext/native/thin3d/thin3d_d3d9.cpp b/ext/native/thin3d/thin3d_d3d9.cpp
index 118bd48fab..3ac3058575 100644
--- a/ext/native/thin3d/thin3d_d3d9.cpp
+++ b/ext/native/thin3d/thin3d_d3d9.cpp
@@ -601,6 +601,8 @@ D3D9Context::D3D9Context(IDirect3D9 *d3d, IDirect3D9Ex *d3dEx, int adapterId, ID
 	caps_.tesselationShaderSupported = false;
 	caps_.framebufferBlitSupported = true;
 	caps_.framebufferCopySupported = false;
+	caps_.framebufferDepthBlitSupported = true;
+	caps_.framebufferDepthCopySupported = false;
 	if (d3d) {
 		D3DDISPLAYMODE displayMode;
 		d3d->GetAdapterDisplayMode(D3DADAPTER_DEFAULT, &displayMode);
diff --git a/ext/native/thin3d/thin3d_gl.cpp b/ext/native/thin3d/thin3d_gl.cpp
index 1334a26e2c..36532fabe9 100644
--- a/ext/native/thin3d/thin3d_gl.cpp
+++ b/ext/native/thin3d/thin3d_gl.cpp
@@ -602,6 +602,7 @@ OpenGLContext::OpenGLContext() {
 		caps_.preferredDepthBufferFormat = DataFormat::D24_S8;
 	}
 	caps_.framebufferBlitSupported = gl_extensions.NV_framebuffer_blit || gl_extensions.ARB_framebuffer_object;
+	caps_.framebufferDepthBlitSupported = caps_.framebufferBlitSupported;
 }
 
 OpenGLContext::~OpenGLContext() {
diff --git a/ext/native/thin3d/thin3d_vulkan.cpp b/ext/native/thin3d/thin3d_vulkan.cpp
index 5a371da48f..005523b991 100644
--- a/ext/native/thin3d/thin3d_vulkan.cpp
+++ b/ext/native/thin3d/thin3d_vulkan.cpp
@@ -658,7 +658,10 @@ VKContext::VKContext(VulkanContext *vulkan)
 	caps_.dualSourceBlend = vulkan->GetFeaturesAvailable().dualSrcBlend != 0;
 	caps_.framebufferBlitSupported = true;
 	caps_.framebufferCopySupported = true;
-	caps_.preferredDepthBufferFormat = DataFormat::D24_S8;
+	caps_.framebufferDepthBlitSupported = false;  // Can be checked for.
+	caps_.framebufferDepthCopySupported = true;   // Will pretty much always be the case.
+	caps_.preferredDepthBufferFormat = DataFormat::D24_S8;  // TODO: Ask vulkan.
+
 	device_ = vulkan->GetDevice();
 
 	queue_ = vulkan->GetGraphicsQueue();