Measurements have been made of the vertical velocity and simultaneous temperature fluctuation at fixed points in turbulent, statistically steady convection in water over an ice surface. Convection was confined to a horizontal layer of constant depth that lay under a stably stratified layer. Measurements of vertical velocities less than 1 mm/s were accomplished using a laser-Doppler velocimeter with a frequency-shifted reference beam. Vertical profiles of all relevant one-point moments, including joint temperature-velocity moments, up to third order were obtained. In the stable layer internal gravity waves were observed, and certain aspects of their behaviour were found to agree with existing theoretical analyses. Typical r.m.s. values of the temperature and velocity fluctuations were nearly equal to the appropriate ‘convection’ scales in the convection layer while in the conduction layer immediately above the ice surface they were more nearly equal to the ‘molecular’ scales. All of the observations were consistent with the existence of buoyant plume-like masses which dominated the structure of the flow. An analysis of the data using a conditional averaging technique to determine the mean properties of these masses showed that below the stable layer they accounted for over 80% of the mean-square fluctuations in temperature and velocity.