Tuckett was also one of the first alpinists to explore the Dolomites in Italy; in 1865, together with Douglas William Freshfield, he traversed the Pale di San Martino group in eastern Trentino, crossing the San Martino Dolomites for the first time, a feat which astonished the mountaineering world as they had no maps and little equipment, relying on skill and intuition. In Trentino, the names of Tuckett, Freshfield, John Ball, and Edward Robson Whitwell are remembered as the pioneers who put the Dolomites on the map. In 1871, in the Brenta Dolomites, Tuckett, with Freshfield and guide Devouassou climbed the Cima Brenta (3,150 m) via the Vedretta di Brenta Superiore on the west side; at the time this peak was thought to be the highest summit in the range. The Rifugio Tuckett above Madonna di Campiglio, situated at an altitude of 2,272 metres in the Brenta Dolomites, is named after him, as is the Bocca del Tuckett (2,648 m), a pass between two steep, rocky peaks that may be seen from the hut.