  Randomized benchmarking and variants thereof, which we collectively call RB+,
are widely used to characterize the performance of quantum computers because
they are simple, scalable, and robust to state-preparation and measurement
errors. However, experimental implementations of RB+ allocate resources
suboptimally and make ad-hoc assumptions that undermine the reliability of the
data analysis. In this paper, we propose a simple modification of RB+ which
rigorously eliminates a nuisance parameter and simplifies the experimental
design. We then show that, with this modification and specific experimental
choices, RB+ efficiently provides estimates of error rates with multiplicative
precision. Finally, we provide a simplified rigorous method for obtaining
credible regions for parameters of interest and a heuristic approximation for
these intervals that performs well in currently relevant regimes.
