Anton Simon's Berceuse is a concise, melodically charming work that fits perfectly into the salon tradition. It is notable for its graceful, flowing rhythmic shape that maintains consistent engagement despite its simplicity.
Pay close attention to the pedaling to sustain the arpeggiated figures without blurring the harmonic changes.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse (Op.28 No.1) is rated Henle level 4 of 9 — intermediate repertoire, roughly ABRSM grades 5–6. In the RCM system it corresponds to about level 6.
You should be comfortable at Henle level 4 — meaning you can already play level 3–4 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.28 No.1) lasts about 3 minutes.
Berceuse (Op.28 No.1) 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 Andante by Wolfgang Amadeus Mozart, Blau Veilchen by Richard Eilenberg, Berceuse by Léon Boëllmann — see the full similar-pieces list on this page.