  Motivated by applications to DNA-storage, flash memory, and magnetic
recording, we study perfect burst-correcting codes for the limited-magnitude
error channel. These codes are lattices that tile the integer grid with the
appropriate error ball. We construct two classes of such perfect codes
correcting a single burst of length $2$ for $(1,0)$-limited-magnitude errors,
both for cyclic and non-cyclic bursts. We also present a generic construction
that requires a primitive element in a finite field with specific properties.
We then show that in various parameter regimes such primitive elements exist,
and hence, infinitely many perfect burst-correcting codes exist.
