Actually, since my posting, I found out that it wasn't as simple as "Et voila" because of what I believe is a bug in ArcMap 10.3. For some rasters, the Export Raster Data dialog changes the extent that was set manually to the data frame (by zooming in ArcMap). In my case, it only considered about half the height of the data frame extent! My workaround: zoom far out enough and then export the raster.
After enlarging the raster beyond the extent that I needed (with NoData cells), I have tried to clip it back to a smaller area that I needed, but ArcMap had a problem there too. This data being mainly intermediary for my CellStatistics calculations, it wasn't too much of a problem.
I hope this helps.