The breaking of symmetry due to atomic displacements in the austenite-martensite phase transformation generally leads to their crystallographic incompatibility. Energy minimizing accommodation mechanisms such as martensite twinning have been recently shown to be a source of hysteresis and irreversible plastic deformation. Compatibility between the two phases can however be achieved by carefully tuning lattice parameters through composition change. A dramatic drop in hysteresis and novel microstructures such as a lowering of the amount of twin lamella are then observed. Related theoretical and simulation works also support the existence of such microstructures including peculiar self-accommodating configurations at near-compatibility. We present the transmission electron microscopy (TEM) study of these novel microstructures for the alloy systems Ti₅₀Ni_50-xPd_xand Ti₅₀Ni_50-xAu_xwhere the composition was systemically tuned to approach perfect compatibility. High resolution imaging of the interface between austenite and martensite supplies evidences of compatibility at the atomic level.