Is it possible to limit how much CPU power a process can take?

There is cpulimit tool (also is present in debian repo and should be in other distros).

It's usage is pretty simple:

cpulimit -p PID -l MAX_CPU_LEVEL

You can also use process name, or full path to binary. Details you can find on the man page.

Another way is by using the (relatively) new kernel interface called cgroups (wikipedia article here). It allows more fine grained control of how much cpu/memory/io/etc a process/user/group is allowed to consume.