We report on new observations of Titan with the International Ultraviolet Explorer in the mid-UV range (lambda approximately 220-335 nm). We use these data to determine upper limits for the abundances of simple organic compounds in the gas phase and to further constrain the properties of the high altitude haze on Titan. As a baseline, we adopted the parametrized microphysical model of McKay et al. (1989) which is successful at reproducing Titan's thermal structure while satisfying several other observational constraints in the visible and IR regions. However, we find that such a model--in which all particles at a given altitude are assumed to have the same size--cannot match simultaneously the IUE observations and the visible/IR data, even when allowance is made for a wide range of values in the adjustable parameters. On the other hand, a good overall agreement is obtained when considering a biomodal size distribution, with small haze particles or "polymers" (r < 0.02 micrometer) acting as strong Rayleigh absorbers below 300 nm and larger haze particles (r approximately 0.1-0.5 micrometer) being responsible for the characteristics of the albedo spectrum in the near-UV, visible, and IR regions. This approach is consistent with the results of several previous investigations of the properties of Titan's haze, although our preferred vertical structure for the haze + polymer material somewhat differs from earlier solutions. On the basis of simple dynamical considerations, we adopted a uniformly mixed layer between 150 and 600 km. The IUE data allow us to place fairly stringent constraints on the abundance of the Rayleigh absorbers, if we assume that their optical properties are similar to those of laboratory-synthesized "tholins": The column-mass density of this material--the essential observable that can be determined from our study--is of the order of 5 micrograms cm-2. This would correspond to number-densities between 10(3) and 10(7) cm-3 in the 150-600 km altitude range, if the average particle radius is between 0.001 and 0.02 micrometer. Such high number densities are a priori at odds with the estimated coagulation lifetime for particles of that size. Thus, our proposed bimodal size distribution is plausible only if inhibiting processes act to slow down considerably the coagulation of polymers in Titan's stratosphere.