I used to have a hard time with losing whites to the shells, too! I've learned to wait until my eggs are about 2 weeks old from the time I bought them. Bring to boil in pot with a dash of salt, and the water just covering the eggs. Once boiling, turn off burner. Leave pot on burner, and cover. Set timer for 20 minutes. When timer is through, pour out hot water. Shake the pot to crack shells a bit. Fill with cold water, and repeat. Let sit for a few minutes. Then, start peeling! The shells should come right off!