According to my financial advisor, keeping a small amount of mortgage makes not one iota of difference to your credit rating, as it doesn't disappear from your credit score. Therefore, lenders will be able to see that you have had a mortgage and paid it off - they will also be able to see if you had any arrears in the past etc.
On the other side of the coin, as it were, what definitely will improve your credit rating is small and regular spending on a credit card which are always paid off in full every month. This demonstrates "normal" debt patterns and also financial stability.
Unless, of course, you're actually applying for a new credit card as people who always pay off their outstanding balance every month aren't credit companies' target market since they earn next to no revenue from them in monthly interest... :-)