Two highly effective content-adaptive methods for generating Delaunay mesh models of digital images, known as HD1 and HD2, are proposed. The methods are derived from the incremental/decremental mesh-generation framework of Adams by using a non-trivial initial mesh and an improved growth schedule. The higher complexity IID2 method is shown to yield mesh models of superior reconstruction quality compared to competing methods, both in terms of squared error and subjective quality, while the lower complexity IID1 method trades mesh quality in return for a decrease in computational cost.