Make sure that your bowl is perfectly clean, dry, and grease free. It is always best to whisk egg whites at medium speed to ensure that air is incorporated in fine bubbles, giving delicacy and stability to the structure.
If you whisk at high speed, the air is not incorporated in the same way, resulting in a more fragile, less stable mixture, usually with less volume. The eggs must be whisked until they form soft peaks, not stiff peaks, contrary to popular belief (and practice).
The peaks they form will bend over slightly, instead of remaining pertly straight. The texture will be similar to that of shaving foam or styling mousse. When egg whites are whisked to this stage, it is relatively easy to incorporate them into other mixtures.