This paper concerns the forecasting of seasonal intraday time series that exhibit repeating intraweek and intraday cycles. A recently proposed exponential smoothing method involves smoothing a different intraday cycle for each distinct type of day of the week. Similar days are allocated identical intraday cycles. A limitation is that the method allows only whole days to be treated as identical. We introduce a new exponential smoothing formulation that allows parts of different days of the week to be treated as identical. The result is a method that involves the smoothing and initialisation of fewer terms. We evaluate forecasting up to a day ahead using two empirical studies. For electricity load data, the new method compares well with a range of alternatives. The second study involves a series of arrivals at a call centre that is open for a shorter duration at the weekends than on weekdays. Among the variety of methods considered, the new method is the only one that can model in a satisfactory way in this situation, where the number of periods on each day of the week is not the same.