Monte Carlo (MC) methods have become very popular in signal processing during the past decades. The adaptive rejection sampling (ARS) algorithms are well-known MC techniques which draw efficiently independent samples from univariate target densities. The ARS schemes yield a sequence of proposal functions that converge towards the target, so that the probability of accepting a sample approaches one. However, sampling from the proposal pdf becomes more computationally demanding each time it is updated. The parsimonious ARS method, where an efficient trade-off between acceptance rate and proposal complexity is obtained, is proposed. Thus, the resulting algorithm is faster than the standard ARS approach.