We aim to estimate parameters and compare estimation methods for the simple step-stress model with Weibull distributed lifetimes under Type-I right-censoring assuming the cumulative exposure model. We use two different scale parameters and one common shape parameter for the two stress levels. We use maximum likelihood estimation and order restricted Bayesian estimation as two parameter estimation methods. To implement order restriction, we use the bivariate joint order statistics probability density function and the bivariate Jones and Larsen (2004) ordered probability density function as prior distributions. We cannot obtain the posterior density function in closed form; therefore, we perform Metropolis-Hastings Markov Chain Monte Carlo. We develop and demonstrate methods through a simulation study for different combinations of sample sizes, censoring amounts and prior densities, and we further demonstrate through an illustrative example.