The effect of an externally applied stress on the B-H loops of UHV-deposited Fe1-xPdx thin films depend strongly on composition. A uniaxial compressive stress increasingly applied along the easy axis of fcc films (x≳0.31) causes the usual distortion of the easy-axis loop toward the appearance of hard-axis loop. Similar stresses applied to bcc films (x≲0.31), however, produce no significant changes in the easy-axis loop until x approaches 0.31 despite the fact that the magnetostriction coefficient only ranges over a factor of 2 for x≥0.12 (λ≥15× 10-6). This locking of the easy axis in bcc films also affects the strain sensitivity which is 0 in the limit of 0 strain, although it approaches the expected value with increasing strain. Several possible origins for this behavior are discussed.