Star-like light traveling past the stars but much slower than a satellite

My husband and I stepped out on the back deck to look at the stars, and I noticed an area of the sky to the SSW, about 2/3 the way to zenith, where something wasn't quite right.  Almost like there should be a satellite there - was something moving?  That's when my eyes zeroed in on a point of light, like a star, moving very slowly among the stars.  It moved in a mostly straight line almost like a satellite, but much slower - maybe a third the speed.  It may have meandered a bit, but that was hard to say as it was moving so slowly.  It grew dimmer over the course of 2 or 3 minutes, at which time we lost sight of it, it having moved no more than 10 degrees during that time.  I couldn't find anything on heavensabove that would indicate it was a known satellite.  My impression was that it was of an aircraft of some sort, flying at a very, very high altitude.