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Fully coherent x rays can be generated by self-seeding x-ray free electron lasers (XFELs). Self-seeding by a forward Bragg diffraction (FBD) monochromator has been recently proposed [G. Geloni, V. Kocharyan, and E. Saldin, J. Mod. Opt. 58, 1391 (2011)JMOPEW0950-034010.1080/09500340.2011.586473] and demonstrated [J. Amann et al., Nat. Photonics 6, 693 (2012)NPAHBY1749-488510.1038/nphoton.2012.180]. Characteristic time T_{0} of FBD determines the power, spectral, and time characteristics of the FBD seed [Yu. Shvyd’ko and R. Lindberg, Phys. Rev. ST Accel. Beams 15, 100702 (2012)PRABFM1098-440210.1103/PhysRevSTAB.15.100702]. Here we show that for a given electron bunch with duration σ_{e} the spectral flux of the self-seeding XFEL can be maximized, and the spectral bandwidth can be respectively minimized by choosing T_{0}∼σ_{e}/π and by optimizing the electron bunch delay τ_{e}. The choices of T_{0} and τ_{e} are not unique. In all cases, the maximum value of the spectral flux and the minimum bandwidth are primarily determined by σ_{e}. Two-color seeding takes place if T_{0}≪σ_{e}/π. The studies are performed, for a Gaussian electron bunch distribution with the parameters, close to those used in the short-bunch (σ_{e}≃5  fs) and long-bunch (σ_{e}≃20  fs) operation modes of the Linac Coherent Light Source XFEL.