Biophysical tissue models are a solid tool for obtaining specific biomarkers with diffusion MRI. However, the assumptions they rely on are sometimes inaccurate and may lead to erroneous results. Some limitations of the Neurite Orientation Dispersion and Density Imaging (NODDI) model are tackled by NODDIDA (NODDI with Diffusivities Added), at the cost of an extended acquisition protocol. Here we adapt NODDIDA to a Double Diffusion Encoding scheme to improve the parameter estimation for reduced acquisition protocols. We demonstrate through in silico experiments that under similar experimental conditions, this novel approach increases both the accuracy and precision of the parameter estimates.