A novel method is proposed to estimate random parameter logit models using the asymmetric triangular distribution to describe unobserved preference heterogeneity in the population of interest. The asymmetric triangular mixing density has the potential to overcome behavioural limitations associated with the most frequently applied mixing densities like the normal and log-normal distribution. With only three parameters it remains parsimonious whilst its bounded support can easily be brought in line with behavioural intuitions. The triangular mixing density is not associated with an incredibly large upper (or lower) bound and it can accommodate varying degrees of skewness in unobserved preference heterogeneity. The proposed estimation procedure is based on the principle of mixture densities and circumvents additional simulation chatter arising when applying the inverse cumulative density function method to generate draws from the mixing density.