rsync slowness

[Gregory Heytings]

I finally take the time to report an rsync slowness pattern that I've been 
seeing for years.

Assuming:

a directory with many (> 20K) files, for example a maildir, on the sending 
side, and

a partial copy of that directory on the receiving side, with "enough" 
missing missing (say 5K),

then the receiving side will do the following: it will take about one 
minute to start transferring the missing files, and will apparently hang 
about one minute every 200 files or so.  After a few (about 10 or 20) 
iterations, the receiving side apparently hangs.

On the receiving side rsync is using 100% CPU, on the sending side not 
more than a few percents.  In case it matters, both sides are using ext4 
filesystems, and Debian GNU/Linux.

I tried --msgs2stderr -M--msgs2stderr, but that does not print any error 
message, I also tried to disable compression, to use --whole-file, to use 
--no-inc-recursive, ..., to no avail.

Any hints?