diff --git a/src/Magnum/TextureTools/Atlas.cpp b/src/Magnum/TextureTools/Atlas.cpp
index 6ae97c1fb..19bfdab9c 100644
--- a/src/Magnum/TextureTools/Atlas.cpp
+++ b/src/Magnum/TextureTools/Atlas.cpp
@@ -80,8 +80,8 @@ Containers::Pair<Int, Containers::Array<Vector3i>> atlasArrayPowerOfTwo(const Ve
     Containers::Array<Vector3i> sortedSizes{NoInit, sizes.size()};
     for(std::size_t i = 0; i != sizes.size(); ++i) {
         const Vector2i size = sizes[i];
-        CORRADE_ASSERT(size.product() && size.x() == size.y() && (size & (size - Vector2i{1})).isZero(),
-            "TextureTools::atlasArrayPowerOfTwo(): expected size" << i << "to be a non-zero power-of-two square, got" << Debug::packed << size, {});
+        CORRADE_ASSERT(size.product() && size.x() == size.y() && (size & (size - Vector2i{1})).isZero() && size <= layerSize,
+            "TextureTools::atlasArrayPowerOfTwo(): expected size" << i << "to be a non-zero power-of-two square not larger than" << Debug::packed << layerSize << "but got" << Debug::packed << size, {});
 
         sortedSizes[i].xy() = size;
         sortedSizes[i].z() = i;
diff --git a/src/Magnum/TextureTools/Atlas.h b/src/Magnum/TextureTools/Atlas.h
index 1b280b246..d1c5a9f1e 100644
--- a/src/Magnum/TextureTools/Atlas.h
+++ b/src/Magnum/TextureTools/Atlas.h
@@ -60,8 +60,9 @@ std::vector<Range2Di> MAGNUM_TEXTURETOOLS_EXPORT atlas(const Vector2i& atlasSize
     coordinate being the layer index
 @m_since_latest
 
-Both @p layerSize and all items in @p sizes are expected to be non-zero, square
-and power-of-two. With such constraints the packing is optimal with no wasted
+The @p layerSize is expected to be non-zero, square and power-of-two. All items
+in @p sizes are expected to be non-zero, square, power-of-two and not larger
+than @p layerSize. With such constraints the packing is optimal with no wasted
 space in all but the last layer. Setting @p layerSize to the size of the
 largest texture in the set will lead to the least wasted space in the last
 layer.
diff --git a/src/Magnum/TextureTools/Test/AtlasTest.cpp b/src/Magnum/TextureTools/Test/AtlasTest.cpp
index 8027c97ea..d652a38cb 100644
--- a/src/Magnum/TextureTools/Test/AtlasTest.cpp
+++ b/src/Magnum/TextureTools/Test/AtlasTest.cpp
@@ -70,14 +70,25 @@ const struct {
         {0, 2, 7, 13, 11, 3, 4, 5, 8, 14, 1, 9, 6, 12, 10}},
 };
 
+const struct {
+    const char* name;
+    Vector2i size;
+    const char* message;
+} ArrayPowerOfTwoWrongLayerSizeData[]{
+    {"non-power-of-two", {128, 127}, "{128, 127}"},
+    {"non-square", {128, 256}, "{128, 256}"},
+    {"zero", {1024, 0}, "{1024, 0}"},
+};
+
 const struct {
     const char* name;
     Vector2i size;
     const char* message;
 } ArrayPowerOfTwoWrongSizeData[]{
+    {"larger than size", {512, 512}, "{512, 512}"},
     {"non-power-of-two", {128, 127}, "{128, 127}"},
     {"non-square", {128, 256}, "{128, 256}"},
-    {"zero", {1024, 0}, "{1024, 0}"}
+    {"zero", {1024, 0}, "{1024, 0}"},
 };
 
 AtlasTest::AtlasTest() {
@@ -95,8 +106,10 @@ AtlasTest::AtlasTest() {
 
     addTests({&AtlasTest::arrayPowerOfTwoMoreLayers});
 
-    addInstancedTests({&AtlasTest::arrayPowerOfTwoWrongLayerSize,
-                       &AtlasTest::arrayPowerOfTwoWrongSize},
+    addInstancedTests({&AtlasTest::arrayPowerOfTwoWrongLayerSize},
+        Containers::arraySize(ArrayPowerOfTwoWrongLayerSizeData));
+
+    addInstancedTests({&AtlasTest::arrayPowerOfTwoWrongSize},
         Containers::arraySize(ArrayPowerOfTwoWrongSizeData));
 }
 
@@ -274,7 +287,7 @@ void AtlasTest::arrayPowerOfTwoMoreLayers() {
 }
 
 void AtlasTest::arrayPowerOfTwoWrongLayerSize() {
-    auto&& data = ArrayPowerOfTwoWrongSizeData[testCaseInstanceId()];
+    auto&& data = ArrayPowerOfTwoWrongLayerSizeData[testCaseInstanceId()];
     setTestCaseDescription(data.name);
 
     CORRADE_SKIP_IF_NO_ASSERT();
@@ -298,7 +311,7 @@ void AtlasTest::arrayPowerOfTwoWrongSize() {
         {128, 128},
         data.size
     });
-    CORRADE_COMPARE(out.str(), Utility::formatString("TextureTools::atlasArrayPowerOfTwo(): expected size 2 to be a non-zero power-of-two square, got {}\n", data.message));
+    CORRADE_COMPARE(out.str(), Utility::formatString("TextureTools::atlasArrayPowerOfTwo(): expected size 2 to be a non-zero power-of-two square not larger than {{256, 256}} but got {}\n", data.message));
 }
 
 }}}}