hey pstring I wasn't really that clear on that too, but when someone says just harmonics that's what I think of. What I said still fits the situation, you shouldn't leave the finger you use to play the harmonic on the string cause no one can hold the fingers perfectly still so just take them on the strings. Then there is no chance of suppressing the harmonic. Also if the harmonics are not sounding out right check your bridge to make sure it is correctly aligned. here's a way to test that..

Get your tuner and tune say your low E, get it in tune, and now play the same string but on the 12th fret, it should be tuned to E also. If not, you need to adjust our bridge.