Seiffert has defined two well-known trigonometric means denoted by 𝒫 and 𝒯 . In a similar way it was defined by Carlson the logarithmic mean ℒ as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean ℳ . There are more known inequalities between the means 𝒫 , 𝒯 , and ℒ and some power means 𝒜 𝑝 . We add to these inequalities two new results obtaining the following nice chain of inequalities 𝒜 0 < ℒ < 𝒜 1 / 2 < 𝒫 < 𝒜 1 < ℳ < 𝒜 3 / 2 < 𝒯 < 𝒜 2 , where the power means are evenly spaced with respect to their order.