  We apply a messenger field method to solve the linear minimum-variance
mapmaking equation in the context of Cosmic Microwave Background (CMB)
observations. In simulations, the method produces sky maps that converge
significantly faster than those from a conjugate gradient descent algorithm
with a diagonal preconditioner, even though the computational cost per
iteration is similar. The messenger method recovers large scales in the map
better than conjugate gradient descent, and yields a lower overall $\chi^2$. In
the single, pencil beam approximation, each iteration of the messenger
mapmaking procedure produces an unbiased map, and the iterations become more
optimal as they proceed. A variant of the method can handle differential data
or perform deconvolution mapmaking. The messenger method requires no
preconditioner, but a high-quality solution needs a cooling parameter to
control the convergence. We study the convergence properties of this new
method, and discuss how the algorithm is feasible for the large data sets of
current and future CMB experiments.
