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We have obtained spectroscopy and photometry of HD 95559 and photometry of Gliese 410=DS Leonis. HD 95559 consists of a pair of essentially identical K1 V stars, whose orbital period we refine to 1.52599775+/-0.00000104 days. The system is photometrically variable with a mean period of 1.5264+/-0.0003 days. Despite minimum masses greater than 0.8 Msolar for each component, a search for eclipses proved negative. The lithium abundances of the components of HD 95559 indicate that the system is younger than the Hyades cluster, and its components may even have just arrived on the zero-age main sequence. Gl 410=DS Leo is also a photometric variable, but we conclude that the photometric period originally ascribed to this star is an alias of the period for HD 95559. We find periods of 13.99 and 15.71 days for the first and second seasons of observation, respectively. Both HD 95559 and Gl 410 are BY Draconis variables, with variability resulting from the rotational modulation of starspots. We also find HR 4269, the check star for our photometry of HD 95559 and Gl 410, to be a variable K4 III with a photometric period of 26.4 days in the first season of observation and periods of 13.96 and 83 days in the second. We suggest that its variability mechanism is radial pulsation, the same as that for M giant semiregular variables.