Bandlimited optical intensity channels, such as visible light communication (VLC) systems, require that all signals satisfy a bandwidth constraint as well as average and non-negativity amplitude constraints. In this paper, a two-dimensional signal space for optical intensity channels is presented in which all signals are strictly bandlimited. A novel feature of this model is that the strict non-negativity constraint is relaxed and the signal space parameterizes the probability that the resulting output amplitude is negative. The motivation for this relaxation is that even though the optical intensity channel only supports non-negative amplitudes, if the likelihood of a negative amplitude excursion is small enough the impact of clipping or biasing on system performance will be negligible. For a given signal space, the probability that the output signal assumes a negative amplitude is rigorously upperbounded and also numerically found with a tractable and tight approximation. The uncoded power and spectral efficiencies are computed for two-dimensional hexagonal lattice constellations. For a given optical power, constellations developed with the new signal space have larger spectral efficiencies over M-PAM using the minimum bandwidth optical intensity Nyquist pulse.