Yes, there are.
First, have you had this issue before? Does this issue occur only when you start to reach a weight that you need to receive the bar in a full squat? On top of speed, it could also be a confidence issue. I speak from experience when I first started. These few exercises/drills should help:
1. Scarecrow snatches and cleans. I'm not sure if this website has those as demonstration videos, but Greg Everett's book does and the exercises (along with the book) will help you start with becoming more confident in the third pull. To do it, simply grab your bar in your snatch/clean grip and bring your elbows up and outside until your elbow is making roughly a 90-degree angle while you're standing completely erect (as if you were finishing your second pull) with the bar as close to you as possible. This position is obviously a very high position, but it helps simulate where you'll be after the second pull and the path your elbows should travel as you actively reposition yourself under the bar. You can receive the bar in the overhead or rack position and ride it down into a firm squat if you wish to further build that confidence of being in a squatted position.
2. You will get the bar lower as you continue to make progress and build the technique in order to pull yourself quickly under the bar and remain in constant control. Eventually, you'll get down to the tall snatches/cleans, where the bar will rest in your "pockets" (hips in the snatch, upper thigh for the clean) and you'll do the same thing: pull yourself under the bar. At this point, you'll have a clear understanding of where the bar should be and how the rest of your body should react simply because because you've progressed from higher points. This exercise, in my opinion, is the best way to help build your speed under the bar. As the weight becomes heavier, you won't be able to remain as tall, so go to hang positions as needed (a bend at the hips, the slighter the bend the better if you're working speed under the bar)
Be prepared to struggle with stability and receiving the bar, especially in the snatch. The trick is to not get frustrated and don't rush your progression down to the tall position. Give it the time and focus and you'll reap big rewards.
I hope this helps you.
Javier A. Sanjuan
Olympus Barbell Club
Dear God, please help me lift heavy and be awesome. Thanks. Amen.