Modified restricted sequential plans with the potential for early stopping and expected stopping times close to those of the SPRT are given for testing binomial distributions.These plans are based upon the conditional probability of rejecting the null hypothesis given the accumulated data. A normal diffusion process approximation to the binomial random walk is used to obtain the conditional probabilities at each stage of the trial and thusdetermine an acceptance boundary for the null hypothesis. Plans derived using the diffusion process are compared with plans obtained by an exact method in terms of error probabilities and stopping time distributions. Some limiting relationships are also examined.