New techniques for computing the large-signal behaviour of multicavity klystron amplifiers have shown how significant increases in their efficiency can be realised in practice. The computing methods have further benefits of increased speed and accuracy in comparison with previous techniques. A new compressible-cylinder model of the electron beam has been developed, together with a technique for the direct summation of the power transferred to the output cavity. With the new model, space-charge force is evaluated quickly enough for both final gap voltage and final drift length to be set for maximum efficiency independently, and, typically, within half a minute on a fast computer. The rapid determination of best efficiency then permits repeated runs to find the influence of other design parameters, within reasonable totals of computer time. Optimisation of efficiency by computer-controlled variation of design parameters has also been investigated, but its inherent limitations make it unlikely to yield optimum sets of parameters inexpensively. An experimental 4-cavity klystron for u.h.f. t.v. transmission has shown saturated efficiency of 51%, compared with typical values for existing tubes of 35–40%; the tube outline and external circuitry were unchanged, while the t.v. performance was demonstrated to be similar to that of the standard tubes.