  Purpose: Stimulated echo acquisition mode (STEAM) diffusion MRI can be
advantageous over pulsed-gradient spin-echo (PGSE) for diffusion times that are
long compared to $\ttwo$. It is important therefore for biomedical diffusion
imaging applications at 7T and above where $\ttwo$ is short. However, imaging
gradients in the STEAM sequence contribute much greater diffusion weighting
than in PGSE, but are often ignored during post-processing. We demonstrate here
that this can severely bias parameter estimates.
  Method: We present models for the STEAM signal for free and restricted
diffusion that account for crusher and slice-select (butterfly) gradients to
avoid such bias. The butterfly gradients also disrupt experiment design,
typically by skewing gradient-vectors towards the slice direction. We propose a
simple compensation to the diffusion gradient vector specified to the scanner
that counterbalances the butterfly gradients to preserve the intended
experiment design.
  Results: High-field data fixed from a monkey brain experiments demonstrate
the need for both the compensation during acquisition and correct modelling
during post-processing for both diffusion tensor imaging and ActiveAx
axon-diameter index mapping. Simulations support the results and indicate a
similar need in in-vivo human applications.
  Conclusion: Correct modelling and compensation are important for practical
applications of STEAM diffusion MRI.
