diff --git a/axe.d.ts b/axe.d.ts
index 1d0ad14fc2..789f35d1a8 100644
--- a/axe.d.ts
+++ b/axe.d.ts
@@ -12,6 +12,8 @@ declare module axe {
 
 	type RunOnlyType = "rule" | "rules" | "tag" | "tags";
 
+	type RunCallback = (error: Error, results:AxeResults) => void;
+
 	interface ElementContext {
 		node?: Object,
 		selector?: string,
@@ -26,6 +28,13 @@ declare module axe {
 		}
 		values?: TagValue[]
 	}
+	interface RunOptions {
+		runOnly?: RunOnly,
+		rules?: Object,
+		iframes?: Boolean,
+		elementRef?: Boolean,
+		selectors?: Boolean
+	}
 	interface AxeResults {
 		url: string,
 		timestamp: string,
@@ -117,12 +126,18 @@ declare module axe {
 	/**
 	 * Runs a number of rules against the provided HTML page and returns the resulting issue list
 	 *
-	 * @param  {Object}   context  Optional The `Context` specification object @see Context
-	 * @param  {Array}    options  Optional Options passed into rules or checks, temporarily modifying them.
-	 * @param  {Function} callback Optional The function to invoke when analysis is complete.
-	 * @returns {any}  	  results  If the callback was not defined, aXe will return a Promise instead.
+	 * @param   {ElementContext} context  Optional The `Context` specification object @see Context
+	 * @param   {RunOptions}     options  Optional Options passed into rules or checks, temporarily modifying them.
+	 * @param   {RunCallback}    callback Optional The function to invoke when analysis is complete.
+	 * @returns {Promise<AxeResults>|void} If the callback was not defined, aXe will return a Promise.
 	 */
-	function run(context?: ElementContext, options?: {runOnly?: RunOnly, rules?: Object, iframes?: Boolean, elementRef?: Boolean, selectors?: Boolean}, callback?: (error: Error, results:AxeResults) => void): any
+	function run(context: ElementContext): Promise<AxeResults>
+	function run(options: RunOptions): Promise<AxeResults>
+	function run(callback: (error: Error, results:AxeResults) => void): void
+	function run(context: ElementContext, callback: RunCallback): void
+	function run(options: RunOptions, callback: RunCallback): void
+	function run(context: ElementContext, options: RunOptions): Promise<AxeResults>
+	function run(context: ElementContext, options: RunOptions, callback: RunCallback): void
 
 	/**
 	 * Starts analysis on the current document and its subframes