The Fenix P2D is pretty nice.I have found it impossible to use the multiple modes of the P1D one handed.You can also lock the P2D in turbo mode so you only get that or strobe.Don't have one but I agree the P1CE looks nice and should work one handed OK since there is only one brightness setting.
.....oh sorry I just noticed you had the under 60 dollar limit as this rules out the KL4.
If you can find one of the old Nuwai Q3 lights these were very popular around here for a long time. They are easy to mod and do well on rechargeable 123 cells. I really do not remember what they were going for as far as cost however I believe it was about 30 dollars.