It depends on the structure or geometry you are dealing with. Sometimes tetrahedral element may give you better solution compare to other element type like hexahedral,etc.
I like to know what shortcomings of tetrahedral element you are facing while solving problems in FEM ?
In some cases tetra are the only possible way to discretize complex geometries. However, it is strongly suggested, to partition as much as possible your domain and to use hexa wherever is possible (partitions)...
From Abaqus 6.14 User's Guide: "In three dimensions use hexahedral (brick-shaped) elements wherever possible. They give the best results for the minimum cost. Complex geometries can be difficult to mesh completely with hexahedrons; therefore, wedge and tetrahedral elements may be necessary. The linear versions of these elements, C3D4 and C3D6, are poor elements (fine meshes are needed to obtain accurate results); as a result, these elements should generally be used only when necessary to complete a mesh, and, even then, they should be far from any areas where accurate results are needed. "
" You should not use a mesh containing only linear tetrahedral elements (C3D4): the results will be inaccurate unless you use an extremely large number of elements."