Transmission shifting issues

First to second shift fine, between second to third shift sometimes engine will rev up about 50 - 100 rpm, more often right at fifteen miles per hour, only intermittent. Always does this the first shift on cold start. Above 15 mph most of the time is okay. Sometimes slips after the shift, if accelerated too fast. If I am careful will work normal. Do you think new clutches and bands would fix it? Think any hard parts are hurt? What about valve body function?