Palazzo Piatti-Regehnzani owes its nickname - casa del Cucò - to its restorer Antonio Reghenzani (known as "Cucò") who, in the early 20th century, implemented a series of interventions on the structure.

A surviving part of the palace of the Piatti family, who, between the 15th and 16th centuries, were leading figures in Tellina life, it was bequeathed to Marta Giumelli, wife of Antonio Reghenzani. The late Renaissance-style building was reconstructed on the perimeter of foundations from the Roman and medieval periods and, as mentioned, underwent several modifications by Reghenzani.

The interventions can still be seen today in the perfect faux ashlar of the portico and loggia; in the classically inspired friezes; in the Piatti, Besta, Guicciardi and Gatti coats of arms in the loggia; and in the inscriptions of biblical verses and curious maxims and sentences in various parts of the building.

When Antonio died, the palace passed to his only heir: his daughter Maria. The woman, born in Teglio, died in London in poverty in 1978. A few years later, the property went to the Italian state.

Palazzo Piatti-Reghenzani is now completely renovated and home to the Elisa Branchi municipal library.