  First, we present a combined analysis of ${\rm p}{\rm p} \to \mu^+ \nu_\mu
{\rm e}^- \bar \nu_{\rm e}$ and ${\rm p}{\rm p} \to \mu^+ \nu_\mu {\rm e}^-
\bar \nu_{\rm e} {\rm j}$ at next-to-leading order, including both QCD and
electroweak corrections. Second, we provide all-order predictions for ${\rm
p}{\rm p} \to \mu^+ \nu_\mu {\rm e}^- \bar \nu_{\rm p}+\mathrm{jets}$ using
merged parton-shower simulations that also include approximate EW effects. A
fully inclusive sample for WW production is compared to the fixed-order
computations for exclusive zero- and one-jet selections. The various
higher-order effects are studied in detail at the level of cross sections and
differential distributions for realistic experimental set-ups. Our study
confirms that merged predictions are significantly more stable than the
fixed-order ones in particular regarding ratios between the two processes.
