We present experimental and theoretical evidence of thermoelastic martensites in Fe29Ni18Co4Ti alloys. In this class of alloys, the high strength in the austenite domains limits the slip deformation as verified with transmission electron microscopy. The restriction of slip permits a higher degree of recoverability of the transformation. Using both single crystals with  orientation and polycrystals, the appearance of martensite plates upon deformation, and their reversion back to austenite upon heating (the shape memory effect), is revealed with in-situ optical microscopy. Theoretical results for the transformation strains and the detwinning of martensite are presented, which demonstrate convincingly the potential of these classes of alloys. Electrical resistance measurements identified the stress and temperature levels at the onset of forward and reverse transformations in isothermal deformation and thermal cycling experiments, respectively. The return of the electrical resistance to its reference value. upon austenite to martensite followed by martensite to austenite transformation, verified the recovery in the transformation strains measured in the experiments.