In the first half of the 17th 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 CretaSacra, the foundation of the dependency dates back to the early 16th 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 13th Directorate of Byzantine Monuments.