We present a new technique for reconstructing the instantaneous velocity profiles during creep, dynamic, or ramp tests under controlled stress in wide-gap Couette flows, from a series of similar tests under smaller stress amplitudes. This approach is based on a rigourous theory, and since it requires that the fluid does not flow close to the outer cylinder, it is particularly suitable for yield stress fluids. The interest of this reconstruction technique is that it is simpler than direct techniques (nuclear magnetic resonance, light scattering, particle imaging velocimetry, etc.) and has almost no limitations in time and space resolution. Thus, one can obtain the velocity profiles under steady-state and transient flows. We show that for a commercial hair gel the velocity profile obtained with this technique is in excellent agreement with that found from magnetic resonance imaging rheometry within the range of measurement (four decades of velocity). From other tests with a mustard and a kaolin-water suspension we demonstrate that the "viscosity bifurcation" effect observed with various pasty materials [Coussot et al., Phys. Rev. Lett. (2002a)] is directly associated with an abrupt change in the slope of the velocity profiles at the interface between the sheared and unsheared regions. We also show that the effect of wall slip on the reconstructed velocity profile is to shift the level of the unsheared region to a virtual, constant, finite, velocity level. (C) 2004 The Society of Rheology.