In binaural loudness summation, diotic presentation of a sound usually produces approximately double the loudness of monotic presentation. However, experiments using loudspeaker presentation with and without earplugs find that magnitude estimates of loudness are little altered by the earplug, suggesting a form of loudness constancy. We explored the significance of controlling stimulation of the second ear using meatal occlusion as opposed to the deactivation of one earphone. We measured the point of subjective loudness equality (PSLE) for monaural vs. binaural presentation using an adaptive technique for both speech and noise. These stimuli were presented in a reverberant room over a loudspeaker to the right of the listener, or over lightweight headphones. Using the headphones, stimuli were either presented dry, or matched to those of the loudspeaker by convolution with impulse responses measured from the loudspeaker to the listener position, using an acoustic manikin. The headphone response was also compensated. Using the loudspeaker, monotic presentation was achieved by instructing the listener to block the left ear with their finger. Near perfect binaural loudness constancy was observed using loudspeaker presentation, while there was a summation effect of 3-6 dB for both headphone conditions. However, only partial constancy was observed when meatal occlusion was simulated. These results suggest that there may be contributions to binaural loudness constancy from residual low frequencies at the occluded ear as well as a cognitive element, which is activated by the knowledge that one ear is occluded.