Not if they are already leggy. You will need to transplant them into new containers and bury all the stem in the process. Bury the stem up to just below the bottom leaves and roots will develop all along the buried stem.

Then if the light is sufficient they won't turn leggy again but it takes a great deal of light to prevent it and old bulbs loose power. Depending on the number of plants, most of us use multiple 4 foot shop lights with 2 new bulbs each.

Over on the Growing from Seed forum there is a great FAQ and many discussions about light setups.

Dave

Thank you, Dave! I'll give it a go, because these seeds were given to me and aren't available in this country. Darn, wish I'd thought to ask before.

A quick update: I covered up the teeny stems with more planting (starter) mix and they are looking tons better! Most have the first real leaves now, and they look strong and healthy. Still small, but that's ok. I will put them out in the shade for an hour or two starting today, because our temps are so lovely right now.

Watch the wind too.

Thanks, Helenh. I have a covered back porch so I set them on the table near the edge, but out of direct sunlight. There was only a light breeze yesterday and they were fine. Will keep doing so, when I can.