The previously reported simplified cylindrical linear cloak is improved so that the cloak's outer surface is impedance-matched to free space. The scattering characteristics of the improved linear cloak is compared to the previous counterpart as well as the recently proposed simplified quadratic cloak derived from quadratic coordinate transformation. Significant improvement in invisibility performance is noticed for the improved linear cloak with respect to the previously proposed linear one. The improved linear cloak and the simplified quadratic cloak have comparable invisibility performances, except that the latter however has to fulfill a minimum shell thickness requirement (i.e. outer radius must be larger than twice of inner radius). When a thin cloak shell is desired, the improved linear cloak is much more superior than the other two versions of simplified cloaks.