  Codes for correcting sticky insertions/deletions and limited-magnitude errors
have attracted significant attention due to their applications of flash
memories, racetrack memories, and DNA data storage systems. In this paper, we
first consider the error type of $t$-sticky deletions with
$\ell$-limited-magnitude and propose a non-systematic code for correcting this
type of error with redundancy $2t(1-1/p)\cdot\log(n+1)+O(1)$, where $p$ is the
smallest prime larger than $\ell+1$. Next, we present a systematic code
construction with an efficient encoding and decoding algorithm with redundancy
$\frac{\lceil2t(1-1/p)\rceil\cdot\lceil\log p\rceil}{\log p}
\log(n+1)+O(\log\log n)$, where $p$ is the smallest prime larger than $\ell+1$.
