Text entry using gaze-based interaction is a vital communication tool for people with motor impairments. Most solutions require the user to fixate on a key for a given dwell time to select it, thus limiting the typing speed. In this paper we introduce EyeSwipe, a dwell-time-free gaze-typing method. With EyeSwipe, the user gaze-types the first and last characters of a word using the novel selection mechanism "reverse crossing." To gaze-type the characters in the middle of the word, the user only needs to glance at the vicinity of the respective keys. We compared the performance of EyeSwipe with that of a dwell-time-based virtual keyboard. EyeSwipe afforded statistically significantly higher typing rates and more comfortable interaction in experiments with ten participants who reached 11.7 words per minute (wpm) after 30 min typing with EyeSwipe.