Dormancy is commonly separated into a rest period, when the buds remain dormant due to growth-arresting physiological conditions, and a quiescent period, when the buds remain dormant due to unfavourable environmental conditions. A sequential model predicting the number of days during dormancy based on accumulation of chill days during rest and anti-chill days during quiescence is described. Chill days and anti-chill days are calculated using the single triangle method to estimate degree days relative to a threshold temperature. The temperature threshold for calculating the chill and anti-chill days and the chilling requirement to determine when rest is broken are found by trial and error to minimize the root mean square error of predicted and observed bud-burst dates. Using several years of weather and phenological data for cherry, pear, kiwifruit and olive orchards and nine forest species from locations in Sardinia, Italy, the Chill days model performed better than four classical chill unit models and two chilling hour models. The classical chill unit and chilling hour models failed to predict bud-burst in some years depending on the species and climate, whereas the Chill days model always gave good results. The classical chill unit and chilling hour models start to accumulate chilling when temperatures fall below the threshold in autumn, whereas the Chill days model begins to accumulate chilling at a phenological stage (i.e. leaf fall or harvest). Moreover, the classical chill unit and chilling hour models do not separate dormancy into rest and quiescent periods. These factors may partially explain the better performance of the Chill days model. When compared with the null model (using the mean calendar date), the Chill days model gave better results except for the cherry trees and four of the forest species.