For a long time i had that same problem. I couldn't get past it and i know how frusterating it is. The can opener i have now is made by sunbeam (or something like that, it is really common company you can get at walmart) it has white handles, and it is one of those that you put the blade and gear on and squeze the two handles together. It still doesn't work well with the Heiney cans, but i am still looking for a can opener that will. This one will however get the top off of the Heiney cans, but the way it does it is by way of the gear that rotates the cans. The teeth of the gear eventually chew through the outside of the can under the rim (that i wanted to keep on for a tennis ball container lid that fits really good on the top of the Heiney cans) and leaves a rough edge, but it works well on all other cans. I think it was about 6 or 7 dollars. Let me know if you have a good way to get the inside tops off the Heiney cans.