diff --git a/index.js b/index.js
index 5d005c5..847094d 100644
--- a/index.js
+++ b/index.js
@@ -10,8 +10,15 @@ module.exports = function(items, options) {
 	// Clone the items.
 	var newItems = items.map(function(item) { return inPlace ? item : { width: item.width, height: item.height, item: item }; });
 
+	// We need to know whether the widest item exceeds the maximum width.
+	// The optimal sorting strategy changes depending on this.
+	const widestWidth =
+		newItems.sort(function(a, b) { return b.width - a.width})[0].width
+	const widerThanMax = options.maxWidth && (widestWidth > options.maxWidth)
+
 	newItems = newItems.sort(function(a, b) {
-		if (options.maxWidth && !options.maxHeight) return b.width - a.width
+		if (options.maxWidth && !options.maxHeight && widerThanMax) return b.width - a.width
+		if (options.maxWidth && !options.maxHeight) return b.height - a.height
 		if (options.maxHeight) return b.height - a.height
 		// TODO: check that each actually HAS a width and a height.
 		// Sort based on the size (area) of each block.
diff --git a/package.json b/package.json
index bdf22d9..202bc88 100644
--- a/package.json
+++ b/package.json
@@ -1,6 +1,6 @@
 {
   "name": "bin-pack-with-constraints",
-  "version": "1.0.1",
+  "version": "1.0.2",
   "description": "A packing algorithm for 2D bin packing that allows setting a max width or height. Largely based on code and a blog post by Jake Gordon and Bryan Burgers.",
   "author": {
     "name": "Enoch Riese",
diff --git a/packer.growing.js b/packer.growing.js
index 01b9f62..8ed613e 100644
--- a/packer.growing.js
+++ b/packer.growing.js
@@ -33,7 +33,8 @@ Construction:
 	{
 		maxWidth = Infinity: set a max width to constrain the growth in that direction
 		maxHeight = Infinity: set a max height to constrain the growth in that direction
-		TODO strictMax = false: reject blocks that are larger than the max
+		strictMax = false: require wider-than-max blocks to start at left boundary
+		PREVIOUS INTENDED TODO strictMax = false: reject blocks that are larger than the max
 	}
 
 Inputs:
@@ -76,7 +77,7 @@ Example:
 var GrowingPacker = function({maxWidth = Infinity, maxHeight = Infinity, strictMax = false}) {
 	this.maxWidth = maxWidth
 	this.maxHeight = maxHeight
-	// this.strictMax = strictMax
+	this.strictMax = strictMax
 	this.ensureSquare = maxWidth === Infinity && maxHeight === Infinity
 };
 
@@ -87,7 +88,10 @@ GrowingPacker.prototype = {
 		if (len === 0) { return }
 
 		var n, node, block, fit;
-		var width  = this.strictMax && (this.maxWidth < Infinity) ? this.maxWidth : blocks[0].width;
+		// Require wider-than-max blocks to start at the left boundary, so
+		// they encroach past the right boundary minimally.
+		var width  = this.strictMax && (this.maxWidth < Infinity) ? Math.max(blocks[0].width, this.maxWidth) : blocks[0].width;
+
 		var height  = this.strictMax && (this.maxHeight < Infinity) ? this.maxHeight : blocks[0].height;
 		this.root = { x: 0, y: 0, width, height };
 		for (n = 0; n < len ; n++) {
diff --git a/test/test.js b/test/test.js
index 99e2805..4ca33d3 100644
--- a/test/test.js
+++ b/test/test.js
@@ -217,8 +217,48 @@ describe('bin-pack with maxWidth option', function() {
 		assert.equal(result.items.length, bins.length, "Result has same amount of items as the source");
 		verifyResult(result, result.items);
 	})
+})
+
+describe('with strictMax: true', function() {
+	it('packs items that exceed the maximum width at the left edge', function() {
+		var bins = [
+			{ width: 100, height: 10 },
+			{ width: 110, height: 10 },
+		];
+
+		var result = pack(bins, {maxWidth: 90, strictMax: true});
+		assert.ok('items' in result, "Result has items");
+		assert.equal(result.items.length, bins.length, "Result has same amount of items as the source");
+		assert.ok(result.width === 110, 'Width is that of the widest item')
+		verifyResult(result, result.items);
+	})
 
-	describe('with strictMax: true', function() {
-		it('rejects bins that exceed the maximum')
+	it('does not unnecessarily pack items to exceed the maximum width', function() {
+		var bins = [
+			{ width: 10,  height: 110 },
+			{ width: 10,  height: 110 },
+			{ width: 10,  height: 110 },
+			{ width: 40,  height: 48 },
+			{ width: 40,  height: 48 },
+			{ width: 40,  height: 48 },
+			{ width: 50,  height: 48 },
+			{ width: 50,  height: 48 },
+			{ width: 50,  height: 48 },
+			{ width: 60,  height: 48 },
+			{ width: 60,  height: 48 },
+			{ width: 70,  height: 48 },
+			{ width: 70,  height: 48 },
+			{ width: 30,  height: 48 },
+			{ width: 30,  height: 48 },
+			{ width: 30,  height: 48 },
+		];
+
+		var result = pack(bins, {maxWidth: 60, strictMax: true});
+		assert.ok('items' in result, "Result has items");
+		assert.equal(result.items.length, bins.length, "Result has same amount of items as the source");
+		assert.ok(result.width === 70, 'Width is that of the widest item')
+		verifyResult(result, result.items);
 	})
+
+	it('rejects bins that exceed the maximum')
 })