A trend in computer vision today is to retire older, so-called "classic'' methods in favor of ones based on deep neural networks. This has led to tremendous improvements in many areas, but for some problems deep neural solutions may not yet exist or be of practical application. For this and other reasons, classic methods are still widely used in a variety of applications. This paper explores the possibility of using deep neural networks to improve these older methods instead of replace them. In particular, it addresses the issue of parameter selection in these algorithms by using a neural network to predict effective settings on a per-input basis. Specifically, we look at a straightforward and well-understood algorithm with one primary parameter: interactive graph-cut segmentation. This parameter balances region/boundary influences and heavily influences the resulting segmentation. Many approach tuning this parameter by using an ad hoc or empirically selected static setting, while others pre-analyze images to determine effective settings on a per-image basis. Tuning this parameter for each image, or even for each target selection within an image, is highly sensitive to properties of the image and object, suggesting that a network might be able to recognize these properties and predict settings that would improve performance. We employ a lightweight network with minimal layers to avoid adding significant computational overhead with this pre-analysis step. The network predicts the segmentation performance for each of a set of discretely sampled values for this parameter and selects the one with the highest predicted performance. Results demonstrate that this per-image prediction and tuning performs better than a single empirically selected setting.