In the first half of the 17^th century, the Convent of the Virgin Mary Akrotiriani ("of the Headland") stood on the site of the former Tobacco Warehouse, east of the Church of Agia Triada ( the Holy Trinity) and the neighbourhood named after it. It was a dependency of Our Lady Akrotiriani, now Toplou Monastery, near Sitia.

According to Cornelius' work Creta Sacra, the foundation of the dependency dates back to the early 16^th century. The tall, sturdily-built katholikon (principal monastery church) abutted on the northeast corner of the enceinte. The monastery with its substantial defensive wall was recorded on all Venetian maps and was a landmark in that area of the town.

The monastery was demolished in the Ottoman period to make way for a barrack house. This was put to other uses over the course of time, such as a Turkish orphanage, and eventually ended up as a tobacco processing warehouse. The surviving building is entirely Ottoman, but has been extensively modified over time. Following restoration it now houses the offices of the 13^th Directorate of Byzantine Monuments.