What sort of source files are these?
Adobe Premiere is excellent but stupid software. And all advanced NLEs are like that: Vegas, Final Cut, etc. What I mean by that is it edits wonderfully, but the actual processing of the video is lousy. Never use it for deinterlacing, the output defaults are awful, and the import can be wonky.
Simply prep the video be reconverting it to lossless, using VirtualDub
. You likely have a highly compressed H.264 file, and NLEs hate compressed sources.
Mac or Windows?
Adobe Premiere Pro? Elements?
CS version, CC version?