Yesterday morning a very shrill noise, coming from the central air compressor, lasted about 3 or 4 minutes. It hasn't done it today, and is cooling. The kenmore unit is about 10 years old. This is houston tx and it's really hot and humid. Thanks

Sometimes the pressure will make a squeeling noise when it shut off to equlize the pressure. If it is something you have never heard before it may be time to get a tech out and check the pressures on your system. To things you can do yourself is to change the air filter inside and also take a garden hose to the outdoor unit to give it a good cleaning. Dirty coils will lead to high presures

Are you sure it was the compressor, or could it have been from the fan on outdoor unit. If it does it again, go out and try to see what is actually making the noise.