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We present the optical layout of soft X-rays compressors using reflective grating specifically designed to give both
positive or negative group-delay dispersion (GDD). They are tailored for chirped-pulse-amplification experiments with
FEL sources. The optical design originates from an existing compressor with plane gratings already realized and tested at
FERMI, that has been demonstrated capable to introduce tunable negative GDD. Here, we discuss two novel designs for
compressors using deformable gratings capable to give both negative and positive GDD. Two novel designs are
discussed: 1) a design with two deformable gratings and an intermediate focus between the twos, that is demonstrated
capable to introduce positive GDD; 2) a design with one deformable grating giving an intermediate focus, followed by a
concave mirror and a plane grating, that is capable to give both positive and negative GDD depending on the distance
between the second mirror and the second grating. Both the designs are tunable in wavelength and GDD, by acting on
the deformable gratings, that are rotated to tune the wavelength and the GDD and deformed to introduce the radius
required to keep the spectral focus. The deformable gratings have a laminar profile and are ruled on a thin silicon plane
substrate. A piezoelectric actuator is glued on the back of the substrate and is actuated to give a radius of curvature that is
varying from infinite (plane) to few meters. The ruling procedure, the piezoelectric actuator and the efficiency
measurements in the soft X-rays will be presented. Some test cases are discussed for wavelengths shorter than 12 nm.
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