A variant of the Gillette New was the Otto Roth razor. Otto Roth was a German company acquired by Gillette in the early thirties and shortly after that, Gillette decided to make New razors for the US market under the Otto Roth name. To my knowledge, these were specifically the long comb base plates. Although they also had the Common Bar style handle, there were two different types that came with the Otto Roth. One was similar to the one that @efsk
showed in the above post, but had a smooth band on the top of the handle similar to the band on the bottom of the handle. The other handle was a thin Common Bar. The base plate was stamped Otto Roth instead of the Gillette diamond.
Sometime in the late thirties, Germany decided to nationalize the Otto Roth/Gillette factory and so Gillette decided it was a good idea to stop using a German sounding name for razors sold in the US.