Cross sections have been measured with the activation technique at various neutron energies in the range of 16.0 to 20.5 MeV for the following 22 reactions: 19F(n,p)19O, 23Na(n,p)23Ne, 23Na(n,)20F, 25Mg(n,p)25Na, 27Al(n,p)27Mg, 28Si(n,p)28Al, 29Si(n,p)29Al, 29Si(n, np + pn + d)28Al, 31P(n,)28Al, 35Cl(n,2n)34mCl, 37Cl(n,p)37S, 46Ti(n,p)46mSc, 50Ti(n,p)50g+mSc, 51V(n,p)51Ti, 55Mn(n,)52V, 56Fe(n,p)56Mn, 57Fe(n, np + pn + d)56Mn, 57Fe(n,p)57Mn, 93Nb(n,)90mY, 93Nb(n,2n)92mNb, 119Sn(n,p)119gIn, and 138Ba(n,2n)137mBa. The half-lives for the reaction products range from 11 s to 10.15 days. Quasi-monoenergetic neutrons were produced via the 3H(d, n)4He reaction. In some cases isotopically enriched materials were used to enhance the reaction yield or to facilitate correction for interfering reactions leading to the same product. The gamma rays emitted from the irradiated samples were measured with a high-purity germanium detector. A pneumatic sample transport system was used to limit the decay of the radioactive products between neutron irradiation and gamma-ray counting. All cross sections were obtained as ratios to the standard reaction 27Al(n,)24Na, using as secondary neutron fluence references the 27Al(n,p)27Mg reaction as well as a calibrated Bonner sphere. Corrections have been applied for sample-irradiation and counting environment geometric effects, neutron absorption and multiple scattering, time variation of neutron-source strength, neutron-source angular distributions, secondary neutrons from the target, gamma-ray absorption, and gamma-ray sum coincidences. A detailed analysis of the uncertainty sources was performed. The present results are compared with other measurements and evaluated data. For seven reactions, measured cross sections have been obtained for the first time beyond 15 MeV. These new data help appreciably to resolve discrepancies in evaluated data files.