Rudolf Friml, better known for his operettas, composed this modest work in the early 20th century. It features a lush, singing melody supported by a standard hypnotic accompaniment pattern.
The primary challenge is balancing the long, melodic phrases against the subtle left-hand broken chord accompaniment.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse (Op.50) is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 5.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Berceuse (Op.50) lasts about 4 minutes.
Berceuse (Op.50) is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Berceuse by Rudolf Friml, At Twilight by Rudolf Friml, Boola boo by Rudolf Friml — see the full similar-pieces list on this page.