I have a small backyard (18' by 30') and the lawn is several kinds of
grass and has been overrun by crabgrass and clover. There are also
hard bald patches where I can't get grass to grow. It's mostly sun and
the soil is fairly clayish. New York City area.

The local Garden World place suggested ripping it up with a tiller and
putting down lime, starter fertilizer, and seeding. I should then
cover it with some soil so the birds don't eat all the seed. I can
rent a light or medium duty tiller at the local Home Depot and I'll
likely do it this Saturday.

I've read that the existing lawn should be killed with Roundup or
another broadleaf herbicide, but I let my cats go into the yard and
don't want to put down anything that will harm them. They eat the
grass.

So my plan is to till it and try to remove as much of the existing
foliage as possible. It's really only around 400 sq feet of lawn so it
shouldn't be too backbreaking to get the stuff into bags once I rip it
up.

Actually my plan is to do it twice. The first time I get out the old
stuff, then put down the fertilizer and lime and such, and then till
it again to get it all mixed up well. Then seed.

Am I just wasting my time to try this without using Roundup? Should I
be mixing in peat moss?

Any comments greatly appreciated. Thanks.