diff --git a/dlls/wined3d/surface.c b/dlls/wined3d/surface.c
index a43f0f2f2c2..d254e904f8b 100644
--- a/dlls/wined3d/surface.c
+++ b/dlls/wined3d/surface.c
@@ -2522,9 +2522,8 @@ HRESULT texture2d_blt(struct wined3d_texture *dst_texture, unsigned int dst_sub_
             TRACE("Not doing download because of format conversion.\n");
         else if (src_texture->resource.format->conv_byte_count)
             TRACE("Not doing download because the source format needs conversion.\n");
-        else if (wined3d_texture_gl_is_multisample_location(wined3d_texture_gl(src_texture),
-                WINED3D_LOCATION_TEXTURE_RGB))
-            TRACE("Not doing download because of multisample source.\n");
+        else if (!(src_texture->flags & WINED3D_TEXTURE_DOWNLOADABLE))
+            TRACE("Not doing download because texture is not downloadable.\n");
         else if (!texture2d_is_full_rect(src_texture, src_sub_resource_idx % src_texture->level_count, &src_rect))
             TRACE("Not doing download because of partial download (src).\n");
         else if (!texture2d_is_full_rect(dst_texture, dst_sub_resource_idx % dst_texture->level_count, &dst_rect))
diff --git a/dlls/wined3d/texture.c b/dlls/wined3d/texture.c
index 1f9e5817699..380aff5016f 100644
--- a/dlls/wined3d/texture.c
+++ b/dlls/wined3d/texture.c
@@ -1602,9 +1602,15 @@ HRESULT CDECL wined3d_texture_update_desc(struct wined3d_texture *texture, UINT
     if (texture->texture_ops == &texture_gl_ops)
     {
         if (multisample_type && gl_info->supported[ARB_TEXTURE_MULTISAMPLE])
+        {
             wined3d_texture_gl(texture)->target = GL_TEXTURE_2D_MULTISAMPLE;
+            texture->flags &= ~WINED3D_TEXTURE_DOWNLOADABLE;
+        }
         else
+        {
             wined3d_texture_gl(texture)->target = GL_TEXTURE_2D;
+            texture->flags |= WINED3D_TEXTURE_DOWNLOADABLE;
+        }
     }
 
     if (((width & (width - 1)) || (height & (height - 1))) && !d3d_info->texture_npot
@@ -3223,7 +3229,8 @@ static HRESULT wined3d_texture_init(struct wined3d_texture *texture, const struc
     texture->layer_count = layer_count;
     texture->level_count = level_count;
     texture->lod = 0;
-    texture->flags |= WINED3D_TEXTURE_POW2_MAT_IDENT | WINED3D_TEXTURE_NORMALIZED_COORDS;
+    texture->flags |= WINED3D_TEXTURE_POW2_MAT_IDENT | WINED3D_TEXTURE_NORMALIZED_COORDS
+            | WINED3D_TEXTURE_DOWNLOADABLE;
     if (flags & WINED3D_TEXTURE_CREATE_GET_DC_LENIENT)
         texture->flags |= WINED3D_TEXTURE_PIN_SYSMEM | WINED3D_TEXTURE_GET_DC_LENIENT;
     if (flags & (WINED3D_TEXTURE_CREATE_GET_DC | WINED3D_TEXTURE_CREATE_GET_DC_LENIENT))
@@ -3658,6 +3665,9 @@ HRESULT wined3d_texture_gl_init(struct wined3d_texture_gl *texture_gl, struct wi
     if (texture_gl->t.resource.gl_type == WINED3D_GL_RES_TYPE_TEX_RECT)
         texture_gl->target = GL_TEXTURE_RECTANGLE_ARB;
 
+    if (texture_gl->target == GL_TEXTURE_2D_MULTISAMPLE_ARRAY || texture_gl->target == GL_TEXTURE_2D_MULTISAMPLE)
+        texture_gl->t.flags &= ~WINED3D_TEXTURE_DOWNLOADABLE;
+
     return WINED3D_OK;
 }
 
diff --git a/dlls/wined3d/wined3d_private.h b/dlls/wined3d/wined3d_private.h
index dde334cbdbb..71e4d712314 100644
--- a/dlls/wined3d/wined3d_private.h
+++ b/dlls/wined3d/wined3d_private.h
@@ -3506,6 +3506,7 @@ struct wined3d_texture_ops
 #define WINED3D_TEXTURE_DISCARD             0x00002000
 #define WINED3D_TEXTURE_GET_DC              0x00004000
 #define WINED3D_TEXTURE_GENERATE_MIPMAPS    0x00008000
+#define WINED3D_TEXTURE_DOWNLOADABLE        0x00010000
 
 #define WINED3D_TEXTURE_ASYNC_COLOR_KEY     0x00000001