Taking the Bad with the Good.

In my recent Blog, “Pardon My Parroting On,” I mentioned how we started putting some Parrot seed out to attract some local parrots into our backyard and onto our balcony. I also mentioned that it worked better than I could have dreamt it would, and soon we had not only the local parrots but other non-local parrots and rarer birds as well, including the now, not so common, Common Bronze wing Pigeon.
I did not mention the noisy miner, or the common spotted doves, but did mention the Whistling or Crested Pigeon and the pink Galahs. Well these doves, Pigeons and galahs, are now the problem with trying to attract parrots to our Place. Yes we very quickly attracted the desired parrots and a few other desired birds too, but these others soon became problems to us.
The Crested Pigeons, although not native to our area, hang out in a group of up to 20, and the spotted doves, although not normally in groups, are also numerous here and so a lot of seed goes to the wrong birds. And as well, some of the crested pigeons and especially the Galahs, are very bossy and drive away the desired birds and hog the seed for themselves.
Which then leaves us with having to decide between the expensive option of trying to keep seed up to all and sundry, just to try and attract a few desirable birds? Or to feed none and let them all go away?
Over the previous Spring and Summer, we actuality took that latter action, but now in the Winter when some of the desired birds started coming back, we started putting out parrot seed again. And again, quickly re-attracted all the birds we would rather not have! Or at least not have in such large numbers. Thus we have chosen to accept the bad to keep the Good. How would you choose to handle this or a similar situation?