Methods and devices for simultaneously verifying or reading multiple states in non-volatile storage are disclosed. Methods and devices for efficiently reducing or eliminating cross-coupling effects in non-volatile storage are disclosed. Methods and devices for efficiently performing reads at a number of voltages to search for the threshold voltage of a memory cell are disclosed. Memory cells on different NAND strings that are read at the same time may be tested for different threshold voltage levels. Memory cells may be tested for different threshold voltages by applying different gate-to-source voltages to memory cells being tested for different threshold voltages. Memory cells may be tested for different threshold voltages by applying different drain to source voltages to the memory cells. Different amounts of compensation for cross-coupling affects may be applied to memory cells on different NAND strings that are read or programmed at the same time.