Clippers leave lines in fur

I've been shaving LS fur with my new clippers, and have run into a problem; the clippers leave lines in the fur, like crop lines in a field. The clippers are new, I oil and clean them, I don't let them overheat, and I always start with the longest guard I can get away with and slowly work my way down when shaving.

Am I doing something wrong? I will admit that I shave against the grain of the fur (my clippers literally don't pick up the fur otherwise), but it still ends up even and smooth... except for the lines, obviously.
My guess is that my clipper guards are the problem; they are made of plastic, and are thick enough to leave lines of slightly longer fur. I'm thinking about buying some thin, stainless-steel clipper guards, but they are rather expensive.

EDIT: I tried again on a scrap of different fur. It was still LS, but a different brand (higher-quality and thicker). Yes, the clippers still left crop lines, so it's not because of the kind of fur I used.
It's either something I'm doing wrong, or it's the clippers. I'm hoping it's me, because I want to avoid spending more money on new guards or a repair of some kind.

Just for some more info, I am using a pair of Wahl clippers for human hair (not cheapo, but not high-brow either).

Any suggestions for how to fix this would be very appreciated.