Using a novel morphology segregation technique, we observed minority populations ( approximately 3%) of submicron-sized, cluster-dilute fractal-like aggregates, formed in the soot-formation window (fuel-to-air equivalence ratio of 2.0-3.5) of a premixed flame, to have mass fractal dimensions between 1.2 and 1.51. Our observations disagree with previous observations of a universal mass fractal dimension of approximately 1.8 for fractal-like aerosol aggregates formed in the dilute-limit via three-dimensional diffusion-limited cluster aggregation processes. A hypothesis is presented to explain this observation. Subject to verification of this hypothesis, it may be possible to control the fractal dimension and associated properties of aggregates in the cluster-dilute limit through application of a static electric field during the aggregation process.