Feeding wild pigeons - advice needed

Hello,

I recently put up a bird feeder in my garden which has attracted some small birds and I'm very pleased with it.

This attracted the attention of a pigeon, who hangs around underneath while the birds are feeding, picking up any dropped seed.

Feeling sorry for him I now put out a dish of bird seed which he eats and I regularly see him arrive early in the morning.

However, a second pigeon has arrived and instead of sharing the food the first pigeon chases off the second one.

Does anyone have any ideas how I could feed them both so they both get a share of the food?

I could put down two dishes but I'm sure the first pigeon will eat both.

Regards

Kevin