The Coucou-polka is a lighthearted salon piece modeled after the polka dances that were highly fashionable in European drawing rooms. It utilizes simple melodic mimicry to create the 'cuckoo' sound effect.
At Henle 2 this is a beginner-level piece, where steady coordination between the hands is the main hurdle. The main demands: precise articulation — the difference between crisp and blurred is the piece; fine finger independence within the hand; and a waltz lilt that needs charm and a flexible left hand.
Focus on the grace notes and the rhythmic placement of the 'cuckoo' interval to make it distinct.
Comparable difficulty and character — good candidates for what to learn next.
A level or two down with the same spirit — ideal if this piece is still out of reach.
Where this piece's skills lead: slightly harder works making similar technical demands.
Coucou-polka is rated Henle level 2 of 9 — beginner repertoire, roughly ABRSM grades 2–3. In the RCM system it corresponds to about level 2.
You should be comfortable at Henle level 2 — meaning you can already play level 1–2 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 Coucou-polka lasts about 2 minutes.
Coucou-polka 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 Cécily by Frédéric Barbier, Bach-anh-114 by Christian Petzold, Country Dance by Wolfgang Amadeus Mozart — see the full similar-pieces list on this page.