Test if Convert.ChangeType will work between two types

This is a follow-up to this question about converting values with reflection. Converting an object of a certain type to another type can be done like this:

object convertedValue = Convert.ChangeType(value, targetType);

Given two Type instances (say FromType and ToType), is there a way to test whether the conversion will succeed?

E.g. can I write an extension method like this:

public static class TypeExtensions
{
    public static bool CanChangeType(this Type fromType, Type toType)
    {
        // what to put here?
    }
}

EDIT: This is what I have right now. Ugly, but I don't see another way yet...

bool CanChangeType(Type sourceType, Type targetType)
{
  try
  {
    var instanceOfSourceType = Activator.CreateInstance(sourceType);
    Convert.ChangeType(instanceOfSourceType, targetType);
    return true; // OK, it can be converted
  }
  catch (Exception ex)
  {
    return false;
  }