The development of cross-bar H-type cavities (CH-DTL, H21 mode) is ongoing to improve the technology of this attractive type of drift tube linac (DTL). In comparison with the conventional DTL, the H-type cavities can reach a higher effective field gradient and are competitive in shunt impedance at an energy range up to 100 A MeV. H-mode DTL’s profit in shunt impedance additionally when applying the KONUS beam dynamics. They are in use at research laboratories as well as at hospitals. This paper describes a new concept to approach the zero mode in CH-type cavities, by extending the cavity diameter at the tank ends in combination with tilted drift tube stems. RFQs of the four-vane type are operated as well in the H210 mode and the strategy for voltage flattening can be partly applied there too if conventional vane undercuts are causing problems. Up to around 35 MeV, it is attractive to integrate one or more triplet lenses into each cavity, as one KONUS section is relatively short and would not exploit the full rf power of 3 MW klystrons which are available above 300 MHz. Such a cavity is denoted as a coupled CH-cavity CCH. Three possible arrangements of those internal triplet lenses are discussed and are compared to each other. The operating modes as well as higher modes are then compared with a lens-free CH cavity, where the lens position was filled by ordinary drift tubes. As a result, it is shown that the rf behavior and resonance frequency for the higher harmonics of the frequency band are very similar for all four investigated arrays. This means, that the tuning behavior of the CCH cavity can be simply deduced from the lens-free CH cavity by replacing an even number of ordinary drift tubes (nβλ) with a lens-containing drift tube with adequate length and large outer diameter. This large drift tube itself oscillates like an Alvarez-type drift tube. rf simulations on a 30-gap CH cavity show that the reduction in shunt impedance is about 10% when installing a lens with length 2 beta lambda. Published by the American Physical Society 2024