The cheaper ATX power supplies are group regulated, having the 5v (usually) as the control rail. If you have nothing attached to 5v, the output won't be regulated properly, so the 3.3v would oscillate or otherwise be unstable.
Pretty much all cheap power supplies LIE about the output capability, check the labels carefully and assume about 60% of the label is actually possible.
Also, check the label carefully, some say 3.3v 30 A, 5v 20 A , but both added up can do only 100 watts.
The more modern power supplies are 12v-centric , they do 12v only and then use dc-dc converters to get the 3.3v and 5v. These 3.3v and 5v are relatively weak, sometimes as low as 15A on each, but 100-120w both. These modern psus however should give you no problems even if you use only 3.3v for a long time.
You said you bought some good quality atx power supply, could you tell the brand name and model, maybe a link to it? I could possibly tell you more about it if I know the exact model.
You could possibly lower the 5v rail closer to 3.3v depending on the psu, but it would lower then 3.3v and 12v as well (depends on design of psu). I don't think you could lower the 12v rail as low as 3.3v, it would probably be possible to get it to about 6-8 volts.