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We study certain spinning strings exploring the flat directions of AdS3×S3×S3×S1, the massless sector cousins of su(2) and sl(2) sector spinning strings. We describe these, and their vibrational modes, using the D(2,1;α)2 algebraic curve. By exploiting a discrete symmetry of this structure which reverses the direction of motion on the spheres, and alters the masses of the fermionic modes s→κ−s, we find out how to treat the massless fermions which were previously missing from this formalism. We show that folded strings behave as a special case of circular strings, in a sense which includes their mode frequencies, and we are able to recover this fact in the worldsheet formalism. We use these frequencies to calculate one-loop corrections to the energy, with a version of the Beisert–Tseytlin resummation.