  We study electron transport through waveguides (WGs) in which the strengths
of the Rashba ($\alpha$) and Dresselhaus ($\beta$) terms of the spin-orbit
interaction (SOI) vary in space. Subband mixing, due to lateral confinement, is
taken into account only between the two first subbands. For sufficiently narrow
WGs the transmission $T$ exhibits a square-like shape as a function of $\alpha$
or $\beta$. Particular attention is paid to the case of equal SOI strengths,
$\alpha=\beta$, for which spin-flip processes are expected to decrease. The
transmission exhibits resonances as a function of the length of a SOI-free
region separating two regions with SOI present, that are most pronounced for
$\alpha=\beta$. The sign of $\alpha$ strongly affects the spin-up and spin-down
transmissions. The results show that the main effect of subband mixing is to
shift the transmission resonances and to decrease the transmission from one
spin state to another. The effect of possible band offsets between regions that
have different SOI strengths and effective masses is also discussed.
