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How does sieving the soil help?
I think in general you want to consolidate soil with something clay-like, like worm castings, for example - in order to make it fertile and get it to retain water. As it stands, the water percolates downwards just way to easily there.

I sieved my soil to remove countless small stones, builders' rubble and large rocks. Digging in lots of organic matter is the best way to improve the soil

I am way too lazy for that:)

Personally, I don't think small rocks are that much of a big deal. So far, my approach seemed to have worked - with the difference being that last times I practiced this sort of approach I had the luxury of leaving it fallow over Winter and allowing it to compost in place

You are lucky, I was unable to grow anything successfully before I sieved it and dug in lots of organic matter. In fact it will take a few seasons before my soil is even half-way decent. Legumes are about the only thing I can grow successfully in the meantime