  A new class of solutions for Einstein's field equations representing a static
spherically symmetric anisotropic distribution of matter is obtained on the
background of pseudo-spheroidal spacetime. We have prescribed the bounds of the
model parameters $ k $ and $ p_0 $ on the basis of the elementary criteria for
physical acceptability, viz., regularity, stability and energy conditions. By
taking the values of model parameters from the prescribed bounds, we have shown
that our model is compatible with the observational data of a wide variety of
compact stars like 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, PSR
J1614-2230, SMC X-4 and Cen X-3.
