Tumble them in corncob shells or walnut shells, can't remember which one off hand. Have the same issue here...the only problem with tumbling is the media can get into the small holes, and then you have to blow each one out...quite a pia.
For small parts and once in a while use, we use a tumbler from Cabelas, and the media is from Lyman...both for reloading purposes, but we can get a few hundred parts in one batch. For tumbling to actually remove burrs, we have a Burr King bowl type with an assortment of different media and a recirculation system...much better for aggressive use, but the whole lot of Cabelas stuff is less than $75 if I remember correctly.
Steve