Aims.Our aim is to determine the distribution of stellar population parameters (extinction, age, metallicity, and star formation rates) of quiescent galaxies within the rest-frame stellar mass–colour diagrams andUVJcolour–colour diagrams corrected for extinction up toz ∼ 1. These novel diagrams reduce the contamination in samples of quiescent galaxies owing to dust-reddened galaxies, and they provide useful constraints on stellar population parameters only using rest-frame colours and/or stellar mass.Methods.We set constraints on the stellar population parameters of quiescent galaxies combining the ALHAMBRA multi-filter photo-spectra with our fitting code for spectral energy distribution, MUlti-Filter FITting (MUFFIT), making use of composite stellar population models based on two independent sets of simple stellar population (SSP) models. The extinction obtained by MUFFIT allowed us to remove dusty star-forming (DSF) galaxies from the sample of redUVJgalaxies. The distributions of stellar population parameters across these rest-frame diagrams are revealed after the dust correction and are fitted by LOESS, a bi-dimensional and locally weighted regression method, to reduce uncertainty effects.Results.Quiescent galaxy samples defined via classicalUVJdiagrams are typically contaminated by a ∼20% fraction of DSF galaxies. A significant part of the galaxies in the green valley are actually obscured star-forming galaxies (∼30–65%). Consequently, the transition of galaxies from the blue cloud to the red sequence, and hence the related mechanisms for quenching, seems to be much more efficient and faster than previously reported. The rest-frame stellar mass–colour andUVJcolour–colour diagrams are useful for constraining the age, metallicity, extinction, and star formation rate of quiescent galaxies by only their redshift, rest-frame colours, and/or stellar mass. Dust correction plays an important role in understanding how quiescent galaxies are distributed in these diagrams and is key to performing a pure selection of quiescent galaxies via intrinsic colours.