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The introduction of high-entropy alloys (HEA) into the field of shape memory alloys offers enormous potential for improving their functional properties. It is shown how a successive increase in chemical complexity results in strictly monotonically enlarged and increasingly distorted lattices. With increasing the number of elements added to the alloy, the effect of solid solution strengthening appears to be curtailed and first insights into the contribution of additional mechanisms based on lattice distortions are possible. The alloys developed in this study, reaching from ternary NiTiHf to senary TiZrHfCoNiCu, show a great potential to exploit interatomic interactions regarding improvement of functional fatigue. Despite the absence of stress plateaus related to detwinning, recovery effects at loads above 1000 MPa and significant strain recoveries are shown.