Testable scenario for relativity with minimum length

I propose a general class of spacetimes whose structure is governed by obse rver-independent scales of both velocity (c) and length (Planck length), an d I observe that these spacetimes can naturally host a modification of Fitz Gerald-Lorentz contraction such that lengths which in their inertial rest f rame are bigger than a "minimum length" are also bigger than the minimum le ngth in all other inertial frames. With an analysis in leading order in the minimum length, I show that this is the case in a specific illustrative ex ample of postulates for relativity with velocity and length observer-indepe ndent scales. (C) 2001 Elsevier Science B.V. All rights reserved.