A static bootstrap model of baryons including N, N*, Σ, Λ, Y1*, π, and K is considered. The mass difference between the mesons is treated as a parameter. We find one solution which produces strong attractions in several channels expected to be free from bound states, and which therefore seems not self-consistent. Besides, the mass spectrum of this solution differs from the experimental results. It is concluded that the heavier baryons (Ξ, Ξ*, and Ω), and perhaps also the η, are necessary for self-consistency.