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Let $\\overline{\\rho}^{\\mathrm{ab}}$ be the abelianization of $\\overline{\\rho}$ and fix a crystalline lift $\\psi$ of $\\overline{\\rho}^{\\mathrm{ab}}$. We show the existence of a crystalline lift $\\rho$ of $\\overline{\\rho}$ with regular Hodge-Tate weights such that the abelianization of $\\rho$ coincides with $\\psi$. 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Let $\\overline{\\rho}^{\\mathrm{ab}}$ be the abelianization of $\\overline{\\rho}$ and fix a crystalline lift $\\psi$ of $\\overline{\\rho}^{\\mathrm{ab}}$. We show the existence of a crystalline lift $\\rho$ of $\\overline{\\rho}$ with regular Hodge-Tate weights such that the abelianization of $\\rho$ coincides with $\\psi$. 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