Acorn squash (Cucurbita pepo) have been a familiar item at produce stands for decades in the United States and Canada, but little known or appreciated elsewhere. Following the breeding and development of sweet-fleshed acorn squash in Israel and its commercial introduction in 2007, acorn squash became a high-priced, popular produce item there. Scarcity of supply in winter has led to attempts to fill the consumer demand by using available protected cultivation infrastructure in the relatively mild area of southwestern Israel for production. Such production has proven feasible but it was not determined whether it would be preferable to allow the plants to simply grow sprawling on the ground or vertically, using trellises to train the plants to grow erect. Two sweet acorn squash hybrid cultivars differing in fruit size were compared, growing on the ground or on trellises, for yield, quality, and storability of the fruits. The hybrids bore fully ripe fruits from December through February, producing 56% higher yields when trellised rather than when allowed to grow on the ground. The fruits of trellised plants of both hybrids were more uniformly black-green and firmer than those of ground-grown plants. Their dry matter content at harvest and after 78 days of storage was very high, averaging 28% and 25%, respectively. Total soluble solids content of the fruit flesh from trellised plants was 19% at harvest and an extraordinary 20% after storage at 10°C, 70% RH. The fruit flesh of trellised plants was also more highly colored and had higher carotenoid, ascorbate, and anti-oxidant contents. Overall, trellising of sweet acorn squash during the winter under protected cultivation resulted in significantly higher yields and the finest fruit quality.