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We study the one-parameter generalizations of the Starobinsky model of inflation, which obey all observational constraints on the inflationary parameters. Our models are connected to the original Starobinsky model via continuously changing an additional parameter. Modifying the Starobinsky R+R^2 inflationary model by adding an R^{3/2}-term, we find that the tensor-to-scalar ratio significantly increases with raising the parameter in front of that term. The talk is based on the papers V.R. Ivanov, S.V. Ketov, E.O. Pozdeeva and S.Yu. Vernov, JCAP 03 (2022) 058 and E.O. Pozdeeva and S.Yu. Vernov, arXiv:2211.10988.