A Mystery Solved!

The base of the campanile in the Campo Santa Maria del Giglio, Venice
Standing in the Campo Santa Maria del Giglio, in the shadow of the eponymous church, is a plain, brick building, which, nowadays, is used as a souvenir shop. Looking somewhat out of place, it has always aroused my curiosity. It was clearly never intended to be a shop, but what was its original purpose?

The building turns out to be the base of a bell tower, not the remains of one which had fallen down (a common occurrence), but the stump of one which was never built. 

The bell tower was built in the 1680s, but a century later it was deemed to be leaning too much and, in 1775, it was duly demolished. In 1805 work began on rebuilding the bell tower, but it never progressed beyond what we see today. 
Canaletto's painting of Campo Santa Maria del Giglio, Venice
The original campanile can be glimpsed in this painting by Canaletto.