diff --git a/README.md b/README.md
index 28e6907..5883ed3 100644
--- a/README.md
+++ b/README.md
@@ -15,3 +15,4 @@ Gir supports following optimizations:
 
 * Turn runs of +- or <> into one command
 * Turn [-] or [+] into one command
+* Add offsets to commands that modify tape, to reduce moving tape head
diff --git a/gir.js b/gir.js
index 4e58a69..7163ecc 100644
--- a/gir.js
+++ b/gir.js
@@ -8,17 +8,22 @@
 // Unsure if this helps in any way over strings, but I feel it neater
 
 // +++++ → {type: add, value: 5}
+// Can have offset property
 const add = Symbol('add');
 // > → {type: moveHead, value: 1}
 const moveHead = Symbol('moveHead');
 // . → {type: writeByte}
+// Can have offset property
 const writeByte = Symbol('writeByte');
 // , → {type: readByte}
+// Can have offset property
 const readByte = Symbol('readByte');
 // [-] → {type: loop, contents: [{type: add, value: -1}]}
+// Can have isBalanced property
 const loop = Symbol('loop');
 
 // [-] → {type: clear}
+// Can have offset property
 const clear = Symbol('clear');
 
 // TODO: Add extensions from Eldis
@@ -149,30 +154,45 @@ function parse(program) {
 	return parsed;
 }
 
-// ([commandObjects]) <io>
+// ([commandObjects/offsetCommandObjects]) <io>
 function prettyPrint(parsed) {
-	// ([commandObjects], string) <io>
+	// ([commandObjects/offsetCommandObjects], string) <io>
 	function printIndented(parsed, indent = '') {
 		for(let command of parsed) {
 			let line = indent;
 			if(command.type == add) {
 				line += `add ${command.value}`;
+				if('offset' in command) {
+					line += ` (${command.offset})`;
+				}
 				console.log(line);
 			} else if(command.type == moveHead) {
 				line += `moveHead ${command.value}`;
 				console.log(line);
 			} else if(command.type == writeByte) {
 				line += 'writeByte';
+				if('offset' in command) {
+					line += ` (${command.offset})`;
+				}
 				console.log(line);
 			} else if(command.type == readByte) {
 				line += 'readByte';
+				if('offset' in command) {
+					line += ` (${command.offset})`;
+				}
 				console.log(line);
 			} else if(command.type == loop) {
 				line += 'loop';
+				if('isBalanced' in command) {
+					line += ` (balanced: ${command.isBalanced})`;
+				}
 				console.log(line);
 				printIndented(command.contents, indent + '  ');
 			} else if(command.type == clear) {
 				line += 'clear';
+				if('offset' in command) {
+					line += ` (${command.offset})`;
+				}
 				console.log(line);
 			} else {
 				line += `unknown ${command.type}`;
@@ -187,6 +207,8 @@ function prettyPrint(parsed) {
 // Optimization passes
 // ------------------------------------------------------------------
 
+class UnknownIRError extends Error {}
+
 // ([commandObjects]) → [commandObjects]
 function joinAdjacentOps(parsed) {
 	// ([commandObjects], commandType) → [commandObjects]
@@ -255,9 +277,83 @@ function transformClearLoops(parsed) {
 	return optimized;
 }
 
-// ([commandObjects]) → [commandObjects]
+// ([commandObjects]) → [offsetCommandObjects]
+function addOffsetProperties(parsed) {
+	// ([commandObjects]) → {offsetted: [offsetCommandObjects], isBalanced: bool}
+	function worker(parsed) {
+		let offsetted = [];
+		let isBalanced = true;
+		let headChange = 0;
+
+		let offset = 0;
+		for(let command of parsed) {
+			if(command.type == add) {
+				offsetted.push({type: add,
+					value: command.value,
+					offset: offset});
+			} else if(command.type == moveHead) {
+				offset += command.value;
+			} else if(command.type == writeByte) {
+				offsetted.push({type: writeByte,
+					offset: offset});
+			} else if(command.type == readByte) {
+				offsetted.push({type: readByte,
+					offset: offset});
+			} else if(command.type == clear) {
+				offsetted.push({type: clear,
+					offset: offset});
+			} else if(command.type == loop) {
+				// A loop should be self-contained
+				// If offset is not 0, add a moveHead
+				if(offset != 0) {
+					offsetted.push({type: moveHead,
+						value: offset});
+					// Mark we've moved the head
+					headChange += offset;
+				}
+				offset = 0;
+
+				// Run optimization on the loop
+				let result = worker(command.contents);
+				// We're only balanced if our loops are
+				isBalanced = isBalanced && result.isBalanced;
+				offsetted.push({type: loop,
+					contents: result.offsetted,
+					isBalanced: result.isBalanced});
+				// headChange's value becomes invalid if the
+				// loop is not balanced. However, we only
+				// care about its value when figuring out
+				// our isBalanced, which will be forced to
+				// false if any inner loop is not balanced
+			} else {
+				throw new UnknownIRError();
+			}
+		}
+
+		// We need to move the tape head in the end anyways, so
+		// generate moveHead is offseet is not 0
+		if(offset != 0) {
+			offsetted.push({type: moveHead,
+				value: offset});
+		}
+
+		// We're only balanced if relative to start of the loop ends
+		// up as 0
+		isBalanced = isBalanced && offset + headChange == 0;
+
+		return {offsetted, isBalanced};
+	}
+
+	return worker(parsed).offsetted;
+}
+
+// ([commandObjects]) → [offsetCommandObjects]
 function optimize(parsed) {
-	const optimizations = [joinAdjacentOps, transformClearLoops];
+	const optimizations = [
+		joinAdjacentOps,
+		transformClearLoops,
+		addOffsetProperties
+	]
 	return optimizations.reduce((IR, optimization) =>
 		optimization(IR), parsed);
 }