diff --git a/src/Magnum/MeshTools/Test/CompileLinesGLTest.cpp b/src/Magnum/MeshTools/Test/CompileLinesGLTest.cpp
index 2923b146a..99399c653 100644
--- a/src/Magnum/MeshTools/Test/CompileLinesGLTest.cpp
+++ b/src/Magnum/MeshTools/Test/CompileLinesGLTest.cpp
@@ -189,7 +189,9 @@ void CompileLinesGLTest::twoDimensions() {
     CORRADE_COMPARE_WITH(
         _framebuffer.read({{}, {32, 32}}, {PixelFormat::RGBA8Unorm}),
         Utility::Path::join({MESHTOOLS_TEST_DIR, "CompileLinesTestFiles", data.expected}),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences in vertex color rendering on NVidia vs Mesa
+           Intel */
+        (DebugTools::CompareImageToFile{_manager, 0.25f, 0.007f}));
 }
 
 void CompileLinesGLTest::threeDimensions() {
@@ -257,7 +259,9 @@ void CompileLinesGLTest::linePrimitiveCompatibility() {
     CORRADE_COMPARE_WITH(
         _framebuffer.read({{}, {32, 32}}, {PixelFormat::RGBA8Unorm}),
         Utility::Path::join(MESHTOOLS_TEST_DIR, "CompileLinesTestFiles/line-primitive.tga"),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Two/three pixel difference on NVidia vs. Mesa Intel vs Mesa
+           llvmpipe */
+        (DebugTools::CompareImageToFile{_manager, 36.0f, 0.105f}));
 
     _framebuffer.clear(GL::FramebufferClear::Color);
 
@@ -269,7 +273,9 @@ void CompileLinesGLTest::linePrimitiveCompatibility() {
     CORRADE_COMPARE_WITH(
         _framebuffer.read({{}, {32, 32}}, {PixelFormat::RGBA8Unorm}),
         Utility::Path::join(MESHTOOLS_TEST_DIR, "CompileLinesTestFiles/line-primitive.tga"),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Two/three pixel difference on NVidia vs. Mesa Intel vs Mesa
+           llvmpipe */
+        (DebugTools::CompareImageToFile{_manager, 36.0f, 0.07f}));
 
     GL::Renderer::disable(GL::Renderer::Feature::Blending);
 }
diff --git a/src/Magnum/Shaders/Test/LineGLTest.cpp b/src/Magnum/Shaders/Test/LineGLTest.cpp
index cc34b1112..13b249384 100644
--- a/src/Magnum/Shaders/Test/LineGLTest.cpp
+++ b/src/Magnum/Shaders/Test/LineGLTest.cpp
@@ -1360,7 +1360,8 @@ template<LineGL2D::Flag flag> void LineGLTest::renderLineCapsJoins2D() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(image.pixels<Color4ub>()),
         Utility::Path::join({SHADERS_TEST_DIR, "LineTestFiles", data.expected}),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences on NVidia vs Mesa Intel */
+        (DebugTools::CompareImageToFile{_manager, 1.0f, 0.0025f}));
 
     {
         /** @todo drop this when fixed */
@@ -1425,8 +1426,9 @@ void LineGLTest::renderLineCapsJoins2DReversed() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(image.pixels<Color4ub>()),
         Utility::Path::join({SHADERS_TEST_DIR, "LineTestFiles", data.expected}),
+        /* Minor differences on NVidia vs Mesa Intel */
         /** @todo sync this with render2D() once the overlaps are fixed */
-        (DebugTools::CompareImageToFile{_manager, 1.0f, 0.0005f}));
+        (DebugTools::CompareImageToFile{_manager, 1.0f, 0.0025f}));
 }
 
 void LineGLTest::renderLineCapsJoins2DTransformed() {
@@ -1486,7 +1488,8 @@ void LineGLTest::renderLineCapsJoins2DTransformed() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(image.pixels<Color4ub>()),
         Utility::Path::join({SHADERS_TEST_DIR, "LineTestFiles", data.expected}),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences on NVidia vs Mesa Intel */
+        (DebugTools::CompareImageToFile{_manager, 1.0f, 0.0025f}));
 }
 
 template<LineGL3D::Flag flag> void LineGLTest::renderCube3D() {
@@ -1668,7 +1671,8 @@ template<LineGL3D::Flag flag> void LineGLTest::renderCube3D() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(image.pixels<Color4ub>()),
         Utility::Path::join({SHADERS_TEST_DIR, "LineTestFiles", data.expected}),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences on NVidia vs Mesa Intel */
+        (DebugTools::CompareImageToFile{_manager, 1.0f, 0.0031f}));
 }
 
 void LineGLTest::renderPerspective3D() {
@@ -1790,7 +1794,8 @@ template<class T, LineGL2D::Flag flag> void LineGLTest::renderVertexColor2D() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(_framebuffer.read(_framebuffer.viewport(), {PixelFormat::RGBA8Unorm}).pixels<Color4ub>()),
         Utility::Path::join(SHADERS_TEST_DIR, "LineTestFiles/vertex-color.tga"),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences on NVidia vs Mesa Intel */
+        (DebugTools::CompareImageToFile{_manager, 0.34f, 0.0019f}));
 }
 
 template<class T, LineGL3D::Flag flag> void LineGLTest::renderVertexColor3D() {
@@ -1881,7 +1886,8 @@ template<class T, LineGL3D::Flag flag> void LineGLTest::renderVertexColor3D() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(_framebuffer.read(_framebuffer.viewport(), {PixelFormat::RGBA8Unorm}).pixels<Color4ub>()),
         Utility::Path::join(SHADERS_TEST_DIR, "LineTestFiles/vertex-color.tga"),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences on NVidia vs Mesa Intel */
+        (DebugTools::CompareImageToFile{_manager, 0.34f, 0.0019f}));
 }
 
 template<LineGL2D::Flag flag> void LineGLTest::renderObjectId2D() {
@@ -2169,7 +2175,8 @@ template<LineGL2D::Flag flag> void LineGLTest::renderInstanced2D() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(_framebuffer.read(_framebuffer.viewport(), {PixelFormat::RGBA8Unorm}).pixels<Color4ub>()),
         Utility::Path::join(SHADERS_TEST_DIR, "LineTestFiles/instanced.tga"),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences on NVidia vs Mesa Intel */
+        (DebugTools::CompareImageToFile{_manager, 0.67f, 0.001f}));
 
     /* Object ID -- no need to verify the whole image, just check that pixels
        on known places have expected values. SwiftShader insists that the read
@@ -2303,7 +2310,8 @@ template<LineGL3D::Flag flag> void LineGLTest::renderInstanced3D() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(_framebuffer.read(_framebuffer.viewport(), {PixelFormat::RGBA8Unorm}).pixels<Color4ub>()),
         Utility::Path::join(SHADERS_TEST_DIR, "LineTestFiles/instanced.tga"),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences on NVidia vs Mesa Intel */
+        (DebugTools::CompareImageToFile{_manager, 0.67f, 0.001f}));
 
     /* Object ID -- no need to verify the whole image, just check that pixels
        on known places have expected values. SwiftShader insists that the read
@@ -2520,7 +2528,8 @@ void LineGLTest::renderMulti2D() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(_framebuffer.read(_framebuffer.viewport(), {PixelFormat::RGBA8Unorm}).pixels<Color4ub>()),
         Utility::Path::join(SHADERS_TEST_DIR, "LineTestFiles/multidraw.tga"),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences on NVidia vs Mesa Intel */
+        (DebugTools::CompareImageToFile{_manager, 0.67f, 0.00125f}));
 
     /* Object ID -- no need to verify the whole image, just check that pixels
        on known places have expected values. SwiftShader insists that the read
@@ -2734,7 +2743,8 @@ void LineGLTest::renderMulti3D() {
         /* Dropping the alpha channel, as it's always 1.0 */
         Containers::arrayCast<Color3ub>(_framebuffer.read(_framebuffer.viewport(), {PixelFormat::RGBA8Unorm}).pixels<Color4ub>()),
         Utility::Path::join(SHADERS_TEST_DIR, "LineTestFiles/multidraw.tga"),
-        (DebugTools::CompareImageToFile{_manager}));
+        /* Minor differences on NVidia vs Mesa Intel */
+        (DebugTools::CompareImageToFile{_manager, 0.67f, 0.00125f}));
 
     /* Object ID -- no need to verify the whole image, just check that pixels
        on known places have expected values. SwiftShader insists that the read