The ubiquity of heat exchangers makes it worthwhile to perform extensive studies to enhance their performance. Internally finned tubes in heat exchangers are among the most popular devices engineers use to accomplish this goal. Triangular fins are one of the most extensively studied fin shapes in literature. In the present work, we explore the effects of fin truncation on different types of non-uniform triangular fins in turbulent internal flows at a Reynolds number of 20,000. Nonuniform fin designs are generated from triangular fins by selectively truncating either the fin tip, base, or both (for an unbiased comparison). A computational analysis methodology is developed in Ansys Fluent 2022R1 that is validated against empirical correlations for internal pipe flows. For each shape, we vary the fin height and pitch in a wide range to enable the selection of optimal fin geometries. We use the thermal conductance and the pressure loss to quantify performance. We found that truncation at the valley provides the best overall performance, increasing the thermal conductance of triangular fins by 48.8%. Truncation at the tip provides little-to-no performance benefits. We also indicate the effects of the fin height and pitch on the fins' thermo-hydraulic performance.