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This paper is devoted to analyzing the principle and applications of the linear electro-optic (EO) effect for the control of the carrier-envelope-phase (CEP). We introduce and detail here an original method, which relies on the use of an EO dispersive prism pair in a compressor-like configuration. We show that, by choosing an adequate geometry, it is possible to shift the CEP without changing the group delay (isochronous carrier-envelope-phase shifter) or change the induced group delay without varying the CEP. According to our calculations, when applying an electric field around 400 V/cm to the rubidium titanyle phosphate (RTP) prisms in a double pass configuration (2 × 40 mm total length), one obtains a CEP shift of π rad at 800 nm without inducing a group delay. In contrast, this CEP shift is obtained for an electric field around 1.4 kV/cm in a RTP rectangular slab of the same total length and, in this case, the group delay is of the order of a few fs.