A series of (Tb0.2Pr0.8)(x)Dy1-xFe1.93 (0.3 <= x <= 1.0) Laves compounds was prepared using a high-pressure annealing method. These compounds exhibit a multiphase behaviour when prepared by traditional annealing methods whereas they present a single Laves phase when synthesised by high-pressure annealing. The Curie temperature of the Laves compounds decreases with the increasing atomic ratio x. However, the saturation magnetisation does not increase monotonically but goes through a minimum with increasing x. A structural transition from tetragonal to rhombohedral was observed as x increased from 0.6 to 0.7. The magnetostriction decreased slightly with increasing x in the tetragonal phase region and then increased rapidly during the transition from tetragonal to rhombohedral phase at x = 0.7. Furthermore, large low-field magnetostriction and low anisotropy were achieved simultaneously in the (T0.2Pr0.8)(0.7)Dy0.3Fe1.93 compound.