My garden has a moss problem.

What can I put on the lawn, hand spreadable, that will just kill the moss
rather than kill it and feed it?
I've had problems in the past with lawn feeder causing the lawn to require
cutting twice a week.

Also, I get moss in the floor beds and it takes ages to remove. I've tried
hand weeding out the moss and it takes for ever. I then tried using a sieve
and I'm not convinced it all got removed from the soil. Is there a better
method?