I think a simple way would be to include the domain over which you do want solutions. Instead of ending the query with "+not+integer", try ending with "+rational", "+real", or "+complex":
http://api.wolframalpha.com/v2/query?appid=XXXXX&input=solve+%280.2%5E-a+%3D+2*0.4%5E-a+%2B+1+-+2%29+real
This seems to give the behavior/answer you're looking for.