A version of the short-period undulator scheme suggested earlier [A.A. Varfolomeev et al., Nucl. Instr. and Meth. A318 (1992) 809] was investigated experimentally and by simulations. Transverse magnetic field components are provided with this scheme by a redistribution of an external magnetic field supplied by a solenoid similar to that suggested by A.H. Ho et al. (Nucl. Instr. and Meth. A296 (1990) 631]. An enhancement is achieved with an additional set of permanent magnet blocks. 2D simulations using the PANDIRA code and experimental tests with prototype magnets have shown that field values B(w) > 8 kG for a period lambda(w) = 4.5 mm with a 1.5 mm gap can be obtained with a two times lower solenoid field, B(s) = 4 kG. The undulator scheme looks very promising for microundulators.