Gaps in the lawn - When is the best time to overseed?

We seeded the lawn 10 days ago (autumn or spring was not possible if I didn’t want to visit the company multiple times or let the weeds get out of control). In any case, we are watering diligently when it doesn’t rain and you can already see quite a bit of green. Patience is just not my strong suit right now – the gaps so far are worrying me (of course I hope that it will look better in another 10 days or become denser through mowing/branching, etc.).

Anyway: when would you reseed? Before the first mowing? Or maybe only in autumn or next spring, when it’s not so hot and less watering is needed?

Spring 2019

we also still have bare spots, sowed in May, watered 2-3 times every day

Where there is no seed left now, nothing grows anymore, or something else grows there then ;)

I would sow immediately now so that the new seed still germinates before you mow for the first time. It is best to mix the seed with some sand and potting soil -> then it germinates better and can be distributed more evenly.

we also still have bare spots, sowed in May, watered 2-3 times a day

The bare spots might still fill in, but then with the grass species from your seed mixture that are more robust or with the "pioneer species" that are more suited to a cow pasture. This means you will not achieve the same quality in terms of the density of the grass sward in those areas.

Where there is no longer any seed, nothing grows anymore, or rather something else grows there ;)

I would immediately overseed now so that the new seed still germinates before you mow for the first time. Mix the seed best with some sand and potting soil -> then it germinates better and can be distributed more evenly.

How do you come to the conclusion that there is nothing left there? And can you really step on it now (meaning tomorrow, day 11)? Otherwise, it always says that you should not step on it until mowing...? *ponder*