diff --git a/src/render/glyph_atlas.js b/src/render/glyph_atlas.js
index 06df12acf04..f346da9645a 100644
--- a/src/render/glyph_atlas.js
+++ b/src/render/glyph_atlas.js
@@ -1,9 +1,8 @@
 // @flow
 
-import ShelfPack from '@mapbox/shelf-pack';
-
 import { AlphaImage } from '../util/image';
 import { register } from '../util/web_worker_transfer';
+import binpack from '../util/binpack';
 
 import type {GlyphMetrics, StyleGlyph} from '../style/style_glyph';
 
@@ -27,7 +26,6 @@ export default class GlyphAtlas {
 
     constructor(stacks: { [string]: { [number]: ?StyleGlyph } }) {
         const positions = {};
-        const pack = new ShelfPack(0, 0, {autoResize: true});
         const bins = [];
 
         for (const stack in stacks) {
@@ -49,9 +47,8 @@ export default class GlyphAtlas {
             }
         }
 
-        pack.pack(bins, {inPlace: true});
-
-        const image = new AlphaImage({width: pack.w, height: pack.h});
+        const {w, h} = binpack(bins);
+        const image = new AlphaImage({width: w, height: h});
 
         for (const stack in stacks) {
             const glyphs = stacks[stack];
diff --git a/src/render/image_atlas.js b/src/render/image_atlas.js
index 647a4b5dcbb..bcf4e6fc116 100644
--- a/src/render/image_atlas.js
+++ b/src/render/image_atlas.js
@@ -1,9 +1,8 @@
 // @flow
 
-import ShelfPack from '@mapbox/shelf-pack';
-
 import { RGBAImage } from '../util/image';
 import { register } from '../util/web_worker_transfer';
+import binpack from '../util/binpack';
 
 import type {StyleImage} from '../style/style_image';
 
@@ -53,7 +52,6 @@ export default class ImageAtlas {
 
     constructor(images: {[string]: StyleImage}) {
         const positions = {};
-        const pack = new ShelfPack(0, 0, {autoResize: true});
         const bins = [];
 
         for (const id in images) {
@@ -68,9 +66,8 @@ export default class ImageAtlas {
             positions[id] = new ImagePosition(bin, src);
         }
 
-        pack.pack(bins, {inPlace: true});
-
-        const image = new RGBAImage({width: pack.w, height: pack.h});
+        const {w, h} = binpack(bins);
+        const image = new RGBAImage({width: w, height: h});
 
         for (const id in images) {
             const src = images[id];
diff --git a/src/util/binpack.js b/src/util/binpack.js
new file mode 100644
index 00000000000..6bc407aa675
--- /dev/null
+++ b/src/util/binpack.js
@@ -0,0 +1,88 @@
+// @flow
+
+export default function binpack(boxes: Array<{w: number, h: number, x?: number, y?: number}>) {
+    let area = 0;
+    let maxWidth = 0;
+
+    for (const box of boxes) {
+        area += box.w * box.h;
+        maxWidth = Math.max(maxWidth, box.w);
+    }
+
+    // sort the boxes for insertion by height, descending
+    boxes.sort((a, b) => b.h - a.h);
+
+    // aim for a squarish resulting container,
+    // slightly adjusted for sub-100% space utilization
+    const startWidth = Math.max(Math.ceil(Math.sqrt(area / 0.95)), maxWidth);
+
+    // start with a single empty space, unbounded at the bottom
+    const spaces = [{x: 0, y: 0, w: startWidth, h: Infinity}];
+
+    let width = 0;
+    let height = 0;
+
+    for (const box of boxes) {
+        for (let i = spaces.length - 1; i >= 0; i--) {
+            const space = spaces[i];
+
+            // look for empty spaces that can accommodate the current box
+            if (box.w > space.w || box.h > space.h) continue;
+
+            // found the space; add the box to its top-left corner
+            // |-------|-------|
+            // |  box  |       |
+            // |_______|       |
+            // |         space |
+            // |_______________|
+            box.x = space.x;
+            box.y = space.y;
+
+            height = Math.max(height, box.y + box.h);
+            width = Math.max(width, box.x + box.w);
+
+            // if the space matches the box exactly, just remove it
+            if (box.w === space.w && box.h === space.h) {
+                const last = spaces.pop();
+                if (i < spaces.length) spaces[i] = last;
+
+            // if it matches the box height, update the space accordingly
+            // |-------|---------------|
+            // |  box  | updated space |
+            // |_______|_______________|
+            } else if (box.h === space.h) {
+                space.x += box.w;
+                space.w -= box.w;
+
+            // if it matches the box width, update the space accordingly
+            // |---------------|
+            // |      box      |
+            // |_______________|
+            // | updated space |
+            // |_______________|
+            } else if (box.w === space.w) {
+                space.y += box.h;
+                space.h -= box.h;
+
+            // otherwise, update the space accordingly and a new one
+            // |-------|-----------|
+            // |  box  | new space |
+            // |_______|___________|
+            // | updated space     |
+            // |___________________|
+            } else {
+                spaces.push({
+                    x: space.x + box.w,
+                    y: space.y,
+                    w: space.w - box.w,
+                    h: box.h
+                });
+                space.y += box.h;
+                space.h -= box.h;
+            }
+            break;
+        }
+    }
+
+    return {w: width, h: height};
+}