Method overloading in Controller

Since string is nullable, those overloads truly are ambiguous from the standpoint of MVC. Just check if b is null (perhaps make it an optional parameter, if you'd like a default value).

You could, on the other hand, try a custom ActionMethodSelectorAttribute implementation. Here is an example:

public class ParametersRequiredAttribute : ActionMethodSelectorAttribute
    {
        #region Overrides of ActionMethodSelectorAttribute

        /// <summary>
        /// Determines whether the action method selection is valid for the specified controller context.
        /// </summary>
        /// <returns>
        /// true if the action method selection is valid for the specified controller context; otherwise, false.
        /// </returns>
        /// <param name="controllerContext">The controller context.</param><param name="methodInfo">Information about the action method.</param>
        public override bool IsValidForRequest(ControllerContext controllerContext, MethodInfo methodInfo)
        {
            var parameters = methodInfo.GetParameters();

            foreach (var parameter in parameters)
            {
                var value = controllerContext.Controller.ValueProvider.GetValue(parameter.Name);

                if (value == null || string.IsNullOrEmpty(value.AttemptedValue)) return false;
            }

            return true;
        }

        #endregion
    }

Usage:

[ParametersRequired]
public string Download(string a,string b)


// if a & b are missing or don't have values, this overload will be invoked. 
public string Download(string a)

To my mind you should try to use ASP.NET Routing. Just add new MapRoute. You can check example in this post