Time dilation/twin paradox question?

It's a funny one isn't it, and a difficult one to get your head around. A good way of seeing exactly what happens is to imagine the twins sending radio messages to each other at fixed intervals. On the way there, the radio signals are redshifted--the interval is increased, so they come less often than they are sent. On the way home, they are blueshifted--the interval is decreased so they come more often. The travelling twin spends an equal time in redshift and blueshift mode. But the home twin sees a long period of redshift and then a shorter blueshift, so he sees fewer signals come from the astronaut, so he knows the astronaut aged less.