diff --git a/src/Magnum/Text/AbstractGlyphCache.cpp b/src/Magnum/Text/AbstractGlyphCache.cpp
index e7762ffe7..a76205420 100644
--- a/src/Magnum/Text/AbstractGlyphCache.cpp
+++ b/src/Magnum/Text/AbstractGlyphCache.cpp
@@ -366,16 +366,19 @@ void AbstractGlyphCache::flushImage(const Range3Di& range) {
     const Vector3i paddedMax = Math::min(size(),
         range.max() + Vector3i{padding(), 0});
 
+    /* In case a subclass doesn't support image slicing (such as GlyphCacheGL
+       on WebGL 1), it'll set the image as a whole without the storage
+       parameters. In case it doesn't support 3D images (such as GlyphCacheGL
+       on GLES2), it'll clear the row length. OTOH, image height needs to be
+       set even in case of single-layer array images to avoid errors on certain
+       platforms. See GlyphCacheGLTest::setImageArraySingleLayer() for a repro
+       case. */
     /** @todo ugh have slicing on images directly already */
-    PixelStorage storage;
-    storage.setRowLength(state.image.size().x())
-        .setSkip(paddedMin);
-    /* Set image height only if it's an array glyph cache, as otherwise it'd
-       cause errors on ES2 that doesn't support this pixel storage state */
-    if(state.image.size().z() != 1)
-        storage.setImageHeight(state.image.size().y());
     doSetImage(paddedMin, ImageView3D{
-        storage,
+        PixelStorage{}
+            .setRowLength(state.image.size().x())
+            .setImageHeight(state.image.size().y())
+            .setSkip(paddedMin),
         state.image.format(),
         paddedMax - paddedMin,
         state.image.data()});
diff --git a/src/Magnum/Text/DistanceFieldGlyphCacheGL.cpp b/src/Magnum/Text/DistanceFieldGlyphCacheGL.cpp
index 327c2451b..f395a312a 100644
--- a/src/Magnum/Text/DistanceFieldGlyphCacheGL.cpp
+++ b/src/Magnum/Text/DistanceFieldGlyphCacheGL.cpp
@@ -182,13 +182,21 @@ void DistanceFieldGlyphCacheGL::doSetImage(const Vector2i&
     #endif
     #if !(defined(MAGNUM_TARGET_GLES2) && defined(MAGNUM_TARGET_WEBGL))
     {
+        /* If EXT_unpack_subimage is supported, use the storage as-is but
+           reset image height to 0 as that only matters with arrays which are
+           not supported on ES2 at all. It's set by AbstractGlyphCache always
+           because with array textures the upload may fail if not set. See
+           DistanceFieldGlyphCacheGLTest::setImageArraySingleLayer() for a
+           repro case. */
+        PixelStorage storage{image.storage()};
+        storage.setImageHeight(0);
+
         /* The image range was already expanded to include the padding in
            flushImage() */
-        CORRADE_INTERNAL_ASSERT(image.storage().skip().xy() == offset);
-        const Range2Di paddedRange = paddedImageRange(size(), image.storage().skip().xy(), image.size(), ratio);
+        CORRADE_INTERNAL_ASSERT(storage.skip().xy() == offset);
+        const Range2Di paddedRange = paddedImageRange(size(), storage.skip().xy(), image.size(), ratio);
         const ImageView2D paddedImage{
-            PixelStorage{image.storage()}
-                .setSkip({paddedRange.min(), image.storage().skip().z()}),
+            storage.setSkip({paddedRange.min(), storage.skip().z()}),
             image.format(),
             paddedRange.size(),
             image.data()};
diff --git a/src/Magnum/Text/GlyphCacheGL.cpp b/src/Magnum/Text/GlyphCacheGL.cpp
index 61036f5d2..54750ba0e 100644
--- a/src/Magnum/Text/GlyphCacheGL.cpp
+++ b/src/Magnum/Text/GlyphCacheGL.cpp
@@ -157,15 +157,23 @@ void GlyphCacheGL::doSetImage(const Vector2i& offset, const ImageView2D& image)
     #endif
     #if !(defined(MAGNUM_TARGET_GLES2) && defined(MAGNUM_TARGET_WEBGL))
     {
+        /* If EXT_unpack_subimage is supported, use the storage as-is but
+           reset image height to 0 as that only matters with arrays which are
+           not supported on ES2 at all. It's set by AbstractGlyphCache always
+           because with array textures the upload may fail if not set. See
+           GlyphCacheGLTest::setImageArraySingleLayer() for a repro case. */
+        PixelStorage storage{image.storage()};
+        storage.setImageHeight(0);
+
         /* On ES2 if EXT_texture_rg is present, the single-channel texture
            format is Red instead of Luminance */
         #ifdef MAGNUM_TARGET_GLES2
         if(image.format() == PixelFormat::R8Unorm && GL::Context::current().isExtensionSupported<GL::Extensions::EXT::texture_rg>()) {
-            state.texture.setSubImage(0, offset, ImageView2D{image.storage(), GL::PixelFormat::Red, GL::PixelType::UnsignedByte, image.size(), image.data()});
+            state.texture.setSubImage(0, offset, ImageView2D{storage, GL::PixelFormat::Red, GL::PixelType::UnsignedByte, image.size(), image.data()});
         } else
         #endif
         {
-            state.texture.setSubImage(0, offset, image);
+            state.texture.setSubImage(0, offset, ImageView2D{storage, image.format(), image.size(), image.data()});
         }
     }
     #endif