  A calculation of two-electron QED effects to all orders in the nuclear
binding strength parameter $Z\alpha$ is presented for the ground and $n = 2$
excited states of helium-like ions. After subtracting the first terms of the
$Z\alpha$ expansion from the all-order results, we identify the higher-order
QED effects of order $m\alpha^7$ and higher. Combining the higher-order
remainder with the results complete through order $m\alpha^6$ from [V. A.
Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], we obtain the most
accurate theoretical predictions for the ground and non-mixing $n=2$ states of
helium-like ions with $Z = 5-30$. For the mixing $2^1 P_1$ and $2^3 P_1$
states, we extend the previous calculation by evaluating the higher-order
mixing correction and show that it defines the uncertainty of theoretical
calculations in the $LS$ coupling for $Z > 10$.
