As stability increases turbulence becomes more intermittent. A time series of turbulent sensible heat fluxes can then exhibit extended periods with little or no apparent flux ("lulls") punctuated by turbulent "events" with significantly larger flux values. In this analysis times series of turbulent sensible heat fluxes from four sites (one with data from two heights) and gathered during two experiments, CASES99 and VTMX2000, are examined to characterize some features of the intermittency of the fluxes. For convenience, a turbulent flux event can be defined as occurring whenever the sensible heat flux exceeds a specified threshold value for some minimum duration. An intermittency factor f1 can then be defined as the fraction of the time that this threshold value is exceeded over a period of record. The intermittency factor did not show any obvious dependence on median z/L values as stability increased (e.g., z/L >0.5), but, as expected, f1 was found to decrease as the average heat flux for a night decreased, albeit with considerable scatter. Less expected was the finding that f1 tended to decrease linearly with average heat flux when the magnitude of the average became small (e.g., less than 0.01 mK/s.) This linear behavior was found for a range of threshold values and minimum durations, with the slope of the linear relationship decreasing as the duration of an "event" increased. Other properties of intermittent fluxes, including the mean magnitude and duration of events, the mean magnitude and duration of lulls, and the dependence of these quantities on the average flux or intermittency factor are also examined. Possible applications to useful empirical descriptions of turbulence under very stable conditions are considered.