Time-sequenced IUE spectra of a number of bright F-K dwarfs have been used to investigate rotational modulation in several important chromospheric and transition region emission lines. Stellingwerf's phase dispersion minimization (PDM) technique forms the basis of our time series analysis of these sparsely sampled, irregularly spaced observational sequences, which consist of no more than 13 spectra in any one season. In such highly sample-limited time series, the resultant PDM spectrum is greatly complicated by overlapping alias orders which invariably produce strong interference effects, but the deliberately irregular sampling has proven of value in our development of techniques to identify the intrinsic stellar flux modulation period. Two stars are selected to illustrate these new techniques in detail: epsilon Eri, a young, chromospherically active K2 dwarf; and alpha Cen A, an older G2 dwarf with an apparently more quiescent chromosphere. In epsilon Eri, we have found consistently strong indications for a modulation of the UV spectral flux with a period close to 2.8 days from two seasons of observations, with some evidence for persistence of the longitude distribution of active areas over several hundred modulation cycles. This period is 4 times smaller than that reported by the Mount Wilson Ca II monitoring program, and may well be a harmonic of the Mount Wilson period. A somewhat weaker determination is presented for a UV spectral flux modulation period near 29 days in alpha Cen A.