A slow leak in a faucet handle generally happens when the O-rings and/or the gaskets in the handle valve are defective because of corrosion or a tear in the gasket, or there is a restriction in the valve due to mineral deposits. The repair for damaged rings and gaskets is the removal and replacement of the defective O-ring and/or gasket. The replacement parts must match the damaged parts exactly based on the manufacturer and model of the fixture. Replacement parts may be found at your local hardware store and plumbing supply house. If mineral deposits are causing the leaks, it is more practical to replace the faucet valve rather than attempting to clean the valve. These repairs require turning the service water valve OFF and draining the service lines to the fixture PRIOR to the repair. Of course, licensed, and qualified plumbers can assist in this repair.