We present a design-space and three new techniques for head-based interaction with menus in Mixed Reality (MR) with a Head-Mounted Display (HMD). Usual input modalities such as hand gestures and voice commands are not suitable in noisy MR contexts where the users have both hands occupied as in augmented surgery and machine maintenance. To address the two issues of noisy MR contexts and hand-free interaction, we systematically explore the design space of head-controlled menu interaction by considering two design factors: (1) head-controlled menu versus head-controlled cursor (2) virtual targets versus mixed targets anchored on physical objects. Based on the design space, we present three novel menu techniques that we compared with a baseline head-controlled cursor technique. Experimental results suggest that head-controlled menu and head-controlled cursor techniques offer similar performance. In addition, the study found that mixed targets do not impact ultimate user performance when users are trained enough, but improve the learning phase. When using virtual targets, users still progressed after the training phase by reducing their mean selection time by 0.84 s. When using mixed targets, the improvement was limited to 0.3 s.