Today I started a new training regimen with my chess engine, Stockfish.
I played the first 10 moves of 10 games in a row with the White pieces, against Stockfish, set at a search depth of 5 ply (which should equal a rating of about 1600). All games started from 1. e4 e5 2. Nf3 Nc6 3. Bc4. The clocks were set at 10 minutes for each side.
After every move, I looked at the engine evaluation of the position, and at no point did it drop below -1. Mostly it stayed between 0 and 1. I accomplished my aim: to play 10 consecutive games, 10 moves each, keeping the evuluation above -1, at 5 ply. So far, so good.
From here, I will gradually increase the search depth, and the number of moves with the score kept above -1. Naturally, the time allowed will have to be increased as well, and I will have to play other openings too.
This new training method is good, I think. 
Part II
After my first 10 games, I've now played 13 more 10-move/10-minute games against Stockfish. Again with the White pieces, and the same opening, but this time at a search depth of 10 ply (about 2600). I'm resetting my score every time the evalution in a game drops below -1, so I'm not sure how many games I've succeeded in staying above -1, but I think I did it in about half of these 13 games. However, my score is only at 1 now, since I didn't stay above -1 in the game before the last one. I want 10 consecutive games above -1, so 9 more to go without failing. However, I didn't expect to succeed at the equivalent of 2600, and tomorrow I will keep practicing this way, but at a lower level (maybe 6 ply), and with more than 10 moves (most likely 15 in 15 minutes).
Part III
Just played 3 games with White, against Stockfish, same opening as before, but this time at 6 ply, and 15-move games. In all of them I stayed above -1. Above 0 in 2 of them. 
Note: as a rule of thumb 5 ply equals a rating of about 1600. For every ply added, the rating is about 200 points higher. So, 10 ply is about 2600.