diff --git a/lib/instrument/blocks.js b/lib/instrument/blocks.js
index a97ca1aa..367f3d20 100644
--- a/lib/instrument/blocks.js
+++ b/lib/instrument/blocks.js
@@ -99,8 +99,6 @@ function createBlockId(state) {
  * @param {boolean} [props.isSilentConst=false] - `true` if is function expression name,
  *   assignment to which fails silently in sloppy mode
  * @param {boolean} [props.isVar=false] - `true` if defined with `var` statement or function declaration
- * @param {boolean} [props.isFunction=false] - `true` if is function or class name
- *   (relevant as these canot be renamed)
  * @param {boolean} [props.isFrozenName=false] - `true` if is var which is not renamed when used
  *   inside function in which it's bound
  * @param {Array<string>} [props.argNames] - Linked argument names (only relevant for `arguments`)
@@ -125,8 +123,6 @@ function createBinding(block, varName, props, state) {
  * @param {boolean} [props.isSilentConst=false] - `true` if is function expression name,
  *   assignment to which fails silently in sloppy mode
  * @param {boolean} [props.isVar=false] - `true` if defined with `var` statement or function declaration
- * @param {boolean} [props.isFunction=false] - `true` if is function or class name
- *   (relevant as these canot be renamed)
  * @param {boolean} [props.isFrozenName=false] - `true` if is var which is not renamed when used
  *   inside function in which it's bound
  * @param {Array<string>} [props.argNames] - Linked argument names (only relevant for `arguments`)
@@ -139,7 +135,6 @@ function createBindingWithoutNameCheck(block, varName, props) {
 		isConst: !!props.isConst,
 		isSilentConst: !!props.isSilentConst,
 		isVar: !!props.isVar,
-		isFunction: !!props.isFunction,
 		isFrozenName: !!props.isFrozenName,
 		argNames: props.argNames,
 		trails: [] // Trails of usages within same function as binding, where var not function or frozen
diff --git a/lib/instrument/visitors/assignee.js b/lib/instrument/visitors/assignee.js
index 177f2d01..f6f02c3e 100644
--- a/lib/instrument/visitors/assignee.js
+++ b/lib/instrument/visitors/assignee.js
@@ -197,11 +197,7 @@ function IdentifierVar(node, state) {
 		}
 
 		if (fn) fn.bindings.push(binding);
-	} else if (binding.isFunction) {
-		// NB: No need to check `binding.isFrozenName` because it's only set in 2nd pass
-		// so will always be `false` at this point.
-		// Exception would be if it was a shared binding with `arguments`, but this doesn't work yet.
-		// TODO: Add `|| binding.isFrozenName` to `if` condition when that problem is fixed.
+	} else if (binding.isFrozenName) {
 		return;
 	}
 
diff --git a/lib/instrument/visitors/class.js b/lib/instrument/visitors/class.js
index 7e034af2..9951728c 100644
--- a/lib/instrument/visitors/class.js
+++ b/lib/instrument/visitors/class.js
@@ -49,7 +49,7 @@ function ClassDeclaration(node, state, parent, key) {
 	assertNoCommonJsVarsClash(block, className, state);
 	// No need to check for internal var name clash here as will be checked when creating
 	// the binding for class name accessed from inside class
-	createBindingWithoutNameCheck(block, className, {isFunction: true});
+	createBindingWithoutNameCheck(block, className, {isFrozenName: true});
 
 	// Visit class
 	visitClass(node, parent, key, className, state);
diff --git a/lib/instrument/visitors/function.js b/lib/instrument/visitors/function.js
index 36b5d3f6..371b932d 100644
--- a/lib/instrument/visitors/function.js
+++ b/lib/instrument/visitors/function.js
@@ -86,7 +86,7 @@ function FunctionDeclaration(node, state, parent, key) {
 	let binding = block.bindings[fnName];
 	if (!binding) {
 		const isTopLevel = block === hoistBlock;
-		binding = createBinding(block, fnName, {isVar: isTopLevel, isFunction: true}, state);
+		binding = createBinding(block, fnName, {isVar: isTopLevel, isFrozenName: true}, state);
 
 		// If is a sloppy-mode function declaration which may need to be hoisted, record that.
 		// Determine whether to hoist after 1st pass is complete, once all other bindings created.
@@ -99,10 +99,10 @@ function FunctionDeclaration(node, state, parent, key) {
 				parentFn: state.currentFunction
 			});
 		}
-	} else if (!binding.isFunction) {
+	} else if (!binding.isFrozenName) {
 		// Existing binding is a `var` declaration.
-		// Flag binding as a function so `var` declarations' identifiers don't get renamed.
-		binding.isFunction = true;
+		// Flag binding as frozen so `var` declarations' identifiers don't get renamed.
+		binding.isFrozenName = true;
 		binding.trails.length = 0;
 	}
 
@@ -153,7 +153,7 @@ function FunctionExpression(node, state, parent, key) {
  */
 function createAndEnterFunctionOrClassNameBlock(fnName, isSilentConst, state) {
 	const block = createAndEnterBlock(fnName, false, state);
-	createBinding(block, fnName, {isConst: true, isSilentConst, isFunction: true}, state);
+	createBinding(block, fnName, {isConst: true, isSilentConst, isFrozenName: true}, state);
 	return block;
 }
 
@@ -576,10 +576,10 @@ function hoistSloppyFunctionDeclaration(declaration) {
 	// Can be hoisted
 	if (!hoistBlockBinding) {
 		hoistBlock.bindings[varName] = {...declaration.binding, isVar: true};
-	} else if (!hoistBlockBinding.isFunction) {
+	} else if (!hoistBlockBinding.isFrozenName) {
 		// Existing binding is a `var` declaration.
-		// Flag binding as a function so `var` declarations' identifiers don't get renamed.
-		hoistBlockBinding.isFunction = true;
+		// Flag binding as frozen so `var` declarations' identifiers don't get renamed.
+		hoistBlockBinding.isFrozenName = true;
 		hoistBlockBinding.trails.length = 0;
 	}
 }
@@ -726,12 +726,7 @@ function createFunctionInfoFunction(fn, state) {
 	// Compile internal vars and reserved var names
 	const internalVars = Object.create(null),
 		reservedVarNames = new Set();
-	for (const {name: varName, trails, isFunction, isFrozenName} of fn.bindings) {
-		// Function name bindings are not usually added to `fn.bindings`,
-		// but can be included if binding is initially a `var` statement e.g. `var x; function x() {}`.
-		// So skip them here. `parseFunction` adds them to list of reserved var names.
-		if (isFunction) continue;
-
+	for (const {name: varName, trails, isFrozenName} of fn.bindings) {
 		if (isFrozenName && varName !== 'this') {
 			if (!internalVars[varName]) reservedVarNames.add(varName);
 		} else {
@@ -762,13 +757,12 @@ function createFunctionInfoFunction(fn, state) {
 			blockId: block.id,
 			blockName: block.name,
 			vars: mapValues(vars, (varProps, varName) => {
-				const {binding} = varProps;
-				if (varName === 'arguments') argNames = binding.argNames;
+				if (varName === 'arguments') argNames = varProps.binding.argNames;
 				return {
 					isReadFrom: varProps.isReadFrom || undefined,
 					isAssignedTo: varProps.isAssignedTo || undefined,
 					isFrozenName: varProps.isFrozenName || undefined,
-					isFrozenInternalName: binding.isFrozenName || binding.isFunction || undefined,
+					isFrozenInternalName: varProps.binding.isFrozenName || undefined,
 					trails: varProps.trails
 				};
 			})
diff --git a/lib/instrument/visitors/identifier.js b/lib/instrument/visitors/identifier.js
index a4fb9d55..43c277f2 100644
--- a/lib/instrument/visitors/identifier.js
+++ b/lib/instrument/visitors/identifier.js
@@ -167,7 +167,7 @@ function resolveIdentifier(node, block, varName, fn, trail, isReadFrom, isAssign
 
 	// Record if internal var
 	if (block.id >= fn.id) {
-		if (!binding.isFrozenName && !binding.isFunction) binding.trails.push(trail);
+		if (!binding.isFrozenName) binding.trails.push(trail);
 		return;
 	}
 
@@ -179,15 +179,14 @@ function resolveIdentifier(node, block, varName, fn, trail, isReadFrom, isAssign
 		// it will need to be added to `internalVars`.
 		// This is not the case if var is being read from, as an external var is created below,
 		// which will be converted to an internal var.
-		// It's also not needed if binding is a function name or frozen var, as they're not renamed
-		// and so aren't treated as internal vars.
+		// It's also not needed if binding is frozen, as they're not treated as internal vars.
 		// Not possible to know at this point whether binding is frozen or not (an `eval()` might be later
 		// in the function), so store the binding, and type will be changed to `CONST_VIOLATION_NEEDS_NO_VAR`
 		// later on if the binding is frozen.
 		fn.amendments.push({
 			type: binding.isSilentConst && !isStrict
 				? CONST_VIOLATION_SILENT
-				: isReadFrom || binding.isFrozenName || binding.isFunction
+				: isReadFrom || binding.isFrozenName
 					? CONST_VIOLATION_NEEDS_NO_VAR
 					: CONST_VIOLATION_NEEDS_VAR,
 			blockId: block.id,