diff --git a/src/Magnum/Text/AbstractGlyphCache.cpp b/src/Magnum/Text/AbstractGlyphCache.cpp
index 865d29a2b..523a56863 100644
--- a/src/Magnum/Text/AbstractGlyphCache.cpp
+++ b/src/Magnum/Text/AbstractGlyphCache.cpp
@@ -25,6 +25,9 @@
 
 #include "AbstractGlyphCache.h"
 
+#include <Corrade/Containers/StridedArrayView.h>
+#include <Corrade/Containers/ArrayViewStl.h> /** @todo remove once std::vector is gone */
+
 #include "Magnum/Image.h"
 #include "Magnum/ImageView.h"
 #include "Magnum/PixelFormat.h"
@@ -44,7 +47,38 @@ std::vector<Range2Di> AbstractGlyphCache::reserve(const std::vector<Vector2i>& s
     CORRADE_ASSERT((glyphs.size() == 1 && glyphs.at(0) == std::pair<Vector2i, Range2Di>()),
         "Text::AbstractGlyphCache::reserve(): reserving space in non-empty cache is not yet implemented", {});
     glyphs.reserve(glyphs.size() + sizes.size());
-    return TextureTools::atlas(_size, sizes, _padding);
+
+    /* Rotations are not yet supported */
+    TextureTools::AtlasLandfill atlas{_size};
+    atlas.setPadding(_padding)
+         .clearFlags(TextureTools::AtlasLandfillFlag::RotatePortrait|
+                     TextureTools::AtlasLandfillFlag::RotateLandscape);
+
+    /* Create the output array. Because the new atlas packer doesn't accept
+       zero sizes, change those to be (1, 1) instead. A new interface will
+       disallow them as well, but here we want to keep backwards
+       compatibility. */
+    std::vector<Range2Di> out(sizes.size());
+    for(std::size_t i = 0; i != sizes.size(); ++i)
+        out[i].max() = Math::max(sizes[i], Vector2i{1});
+
+    /* The error message matches what the old TextureTools::atlas() did. Not
+       great, but that's the interface we should stay compatible with. */
+    if(!atlas.add(Containers::stridedArrayView(out).slice(&Range2Di::max),
+                  Containers::stridedArrayView(out).slice(&Range2Di::min)))
+    {
+        Error{} << "Text::AbstractGlyphCache::reserve(): requested atlas size"
+                << _size << "is too small to fit" << sizes.size()
+                << "textures. Generated atlas will be empty.";
+        return {};
+    }
+
+    /* Update the ranges max values to match the new offsets, undo the zero
+       sizes being (1, 1) */
+    for(std::size_t i = 0; i != sizes.size(); ++i)
+        out[i].max() = out[i].min() + sizes[i];
+
+    return out;
 }
 
 void AbstractGlyphCache::insert(const UnsignedInt glyph, const Vector2i& position, const Range2Di& rectangle) {
diff --git a/src/Magnum/Text/Test/AbstractGlyphCacheTest.cpp b/src/Magnum/Text/Test/AbstractGlyphCacheTest.cpp
index 2f2187445..b3c7007f1 100644
--- a/src/Magnum/Text/Test/AbstractGlyphCacheTest.cpp
+++ b/src/Magnum/Text/Test/AbstractGlyphCacheTest.cpp
@@ -116,20 +116,31 @@ void AbstractGlyphCacheTest::access() {
 }
 
 void AbstractGlyphCacheTest::reserve() {
-    DummyGlyphCache cache{{29, 20}, {1, 2}};
-
-    std::vector<Range2Di> out = cache.reserve({{5, 3}, {12, 6}, {10, 5}});
+    DummyGlyphCache cache{{24, 20}, {1, 2}};
+
+    /* Padding should get applied to all */
+    std::vector<Range2Di> out = cache.reserve({
+        {5, 3},
+        /* Landscape glyphs shouldn't get rotated */
+        {12, 6},
+        {10, 5},
+        /* Zero-sized glyphs should get preserved */
+        {0, 1},
+        {3, 0},
+    });
     CORRADE_COMPARE_AS(Containers::arrayView(out), Containers::arrayView<Range2Di>({
-        Range2Di::fromSize({1, 2}, {5, 3}),
-        Range2Di::fromSize({15, 2}, {12, 6}),
-        Range2Di::fromSize({1, 12}, {10, 5}),
+        Range2Di::fromSize({6, 12}, {5, 3}),
+        Range2Di::fromSize({1, 2}, {12, 6}),
+        Range2Di::fromSize({13, 12}, {10, 5}),
+        Range2Di::fromSize({1, 17}, {0, 1}),
+        Range2Di::fromSize({1, 12}, {3, 0}),
     }), TestSuite::Compare::Container);
 }
 
 void AbstractGlyphCacheTest::reserveIncremental() {
     CORRADE_SKIP_IF_NO_ASSERT();
 
-    DummyGlyphCache cache{{25, 12}};
+    DummyGlyphCache cache{{24, 20}, {1, 2}};
 
     /* insert() is what triggers the assert, not reserve() alone */
     cache.insert(0, {3, 5}, {{10, 10}, {23, 45}});
@@ -141,12 +152,12 @@ void AbstractGlyphCacheTest::reserveIncremental() {
 }
 
 void AbstractGlyphCacheTest::reserveTooSmall() {
-    DummyGlyphCache cache{{20, 12}};
+    DummyGlyphCache cache{{24, 18}, {1, 2}};
 
     std::ostringstream out;
     Error redirectError{&out};
     CORRADE_VERIFY(cache.reserve({{5, 3}, {12, 6}, {10, 5}}).empty());
-    CORRADE_COMPARE(out.str(), "TextureTools::atlas(): requested atlas size Vector(20, 12) is too small to fit 3 Vector(12, 6) textures. Generated atlas will be empty.\n");
+    CORRADE_COMPARE(out.str(), "Text::AbstractGlyphCache::reserve(): requested atlas size Vector(24, 18) is too small to fit 3 textures. Generated atlas will be empty.\n");
 }
 
 void AbstractGlyphCacheTest::setImage() {