  Measurements of the superconducting upper critical field, H_{c2}, and
critical current density, J_c, have been carried out for MgB_2 doped with Ti
and/or C in order to explore the problems encountered if these dopants are used
to enhance the superconducting performance. Carbon replaces boron in the MgB_2
lattice and apparently shortens the electronic mean free path thereby raising
H_c2. Titanium forms precipitates of either TiB or TiB_2 that enhance the flux
pinning and raise J_c. Most of these precipitates are intra-granular in the
MgB_2 phase. If approximately 0.5% Ti and approximately 2% C are co-deposited
with B to form doped boron fibers and these fibers are in turn reacted in Mg
vapor to form MgB_2, the resulting superconductor has H_{c2}(T=0) ~ 25 T and
J_c ~ 10,000 A/cm**2 at 5 K and 2.2 T.
