Accurate standardization of Type Ia supernovae (SNIa) is instrumental to the usage of SNIa as distance indicators. We analyse a homogeneous sample of 22 lowz SNIa, observed by the Carnegie Supernova Project (CSP) in the optical and near infra-red (NIR). We study the time of the second peak in the J-band, t 2 , as an alternative standardization parameter of SNIa peak optical brightness, as measured by the standard SALT2 parameter m B . We use BAHAMAS, a Bayesian hierarchical model for SNIa cosmology, to estimate the residual scatter in the Hubble diagram.We find that in the absence of a colour correction, t 2 is a better standardization parameter compared to stretch: t 2 has a 1σ posterior interval for the Hubble residual scatter of σ ∆µ = {0.250, 0.257} mag, compared to σ ∆µ = {0.280, 0.287} mag when stretch (x 1 ) alone is used. We demonstrate that when employed together with a colour correction, t 2 and stretch lead to similar residual scatter. Using colour, stretch and t 2 jointly as standardization parameters does not result in any further reduction in scatter, suggesting that t 2 carries redundant information with respect to stretch and colour. With a much larger SNIa NIR sample at higher redshift in the future, t 2 could be a useful quantity to perform robustness checks of the standardization procedure.