  We derive 15 classes of time-dependent two-state models solvable in terms of
the confluent Heun functions. These classes extend over all the known families
of three- and two-parametric models solvable in terms of the hypergeometric and
the confluent hypergeometric functions to more general four-parametric classes
involving three-parametric detuning modulation functions. In the case of
constant detuning the field configurations describe excitations of two-state
quantum systems by symmetric or asymmetric pulses of controllable width and
edge-steepness. The classes that provide constant detuning pulses of finite
area are identified and the factors controlling the corresponding pulse shapes
are discussed. The positions and the heights of the peaks are mostly defined by
two of the three parameters of the detuning modulation function, while the
pulse width is mainly controlled by the third one, the constant term. The
classes suggest numerous symmetric and asymmetric chirped pulses and a variety
of models with two crossings of the frequency resonance. We discuss the
excitation of a two-level atom by a pulse of Lorentzian shape with a detuning
providing one or two crossings of the resonance. We derive closed form
solutions for particular curves in the 3D space of the involved parameters
which compose the complete return spectrum of the considered two-state quantum
system.
