Two recently proposed variants of CD-type discretizations of sea ice dynamics on triangular meshes are implemented in the Finite-VolumE Sea ice-Ocean Model (FESOM version 2). The implementations use the finite element method in spherical geometry with longitude-latitude coordinates. Both are based on the edge-based sea ice velocity vectors but differ in the basis functions used to represent the velocities. The first one uses nonconforming linear (Crouzeix-Raviart) basis functions, and the second one uses continuous linear basis functions on sub-triangles obtained by splitting parent triangles into four smaller triangles. Test simulations are run to show how the performance of the new discretizations compares with the A-grid discretization using linear basis functions. Both CD discretizations are found to simulate a finer structure of linear kinematic features (LKFs). Both show some sensitivity to the representation of scalar fields (sea ice concentration and thickness). Cell-based scalars lead to a finer LKF structure for the first CD discretization, but the vertex-based scalars may be advantageous in the second case.