Frame happens as a result of how you are working with the horse; your horse is in a frame now. If you wish him to be in a different frame, you need to work him in such a way that such a frame occurs naturally - in this case, keeping in mind the training scale.
As such, work on circles and circular lines will help create relaxation, suppleness, and rhythm - the foundation of the training scale, by bending the horse and not allowing them to remain straight and tense. They're also great in that they require further engagement of the horse so as to balance on the circle. Just remember: inside leg to outside rein creating and maintaining that appropriate balance and bend. I always recommend the books 'Progressive Schooling Exercises for Dressage & Jumping' (Islay Auty) and '101 Dressage Exercises for Horse & Rider'. Essentially, any program or set of exercises that is progressive - that progressively teaches the horse to engage and that progressively builds along the training scale.
With a young horse or any horse you're trying to teach to carry itself and collect, your primary goal should be strengthening the hind leg, or developing pushing power - the ability to push forward. Hills, lateral work, poles/cavelleti, transitions - all the usual to develop the hind end. Once you've built up the appropriate strength in the hind limbs, you can start to ask more of the horse by way of engagement of the core, etc, where the horse is progressively carrying itself - carrying power. Lateral work, transitions between and within gaits, progressive circles and lines, etc. The aforementioned books really have some fabulous exercises that take what the horse naturally gives and is capable of, and expands them toward collection.
Really keep in mind the training scale: suppleness, rhythm, contact (initiated by the horse as a result of suppleness and rhythm), impulsion, straightness, and collection. It should be a natural progression 'easy' for the horse as he is developed and conditioned. The initial key/building block is relaxation and softness. The entire process is guided and encouraged by the rider, but that's it - the horse initiates everything from relaxation through to collection, as a result of the process.
....horses should be trained in such a way that they not only love their riders, but look forward to the time they are with them.
~ Xenophon, 350 B.C.
What Naturalequus said. Also, to be clear - straightness happens progressively over time and is relative to the stage of training. It's not something you can say "check!" to and move on. I think where you're really at is the point where you can start developing contact. Bends, transitions within gaits and developing half halts will bring this along.