We propose and investigate a dual-echo (DE) Stejskal-Tanner EPI sequence for rapid DTI-based free water elimination and mapping with explicit T2 modelling (FWET2) in vivo. DTI maps from the DE sequence are artefact-free and similar to the standard, individual echo (IE) approach. Compared to the IE case, an underestimation of T2 values calculated from the DE sequence is observed. The T2 underestimation stems from reduced signal amplitudes in the second echo of the DE sequence, which we demonstrate to correlate with imperfect refocusing RF pulses. A simple correction method is proposed. FWET2 model parameters derived from both sequences are comparable.