Allow non-root process to bind to port 80 and 443?

Is it possible to tune a kernel parameter to allow a userland program to bind to port 80 and 443?

The reason I ask is I think its foolish to allow a privileged process to open a socket and listen. Anything that opens a socket and listens is high risk, and high risk applications should not be running as root.

I'd much rather try to figure out what unprivileged process is listening on port 80 rather than trying to remove malware that burrowed in with root privileges.