Summary: A classical result of Strassen asserts that given probabilities \(\mu , \nu\) on the real line which are in convex order, there exists a martingale coupling with these marginals, i.e. a random vector \((X_1,X_2)\) such that \(X_1\sim \mu\), \(X_2\sim \nu\) and \(\mathbb{E}[X_2|X_1]=X_1\). Remarkably, it is a non-trivial problem to construct particular solutions to this problem. Based on the concept of shadow for measures in convex order, we introduce a family of such martingale couplings, each of which admits several characterizations in terms of optimality properties/geometry of the support set/representation through a Skorokhod embedding. As a particular element of this family we recover the (left-)curtain martingale transport, which has recently been studied (see the first author et al. [Stochastic Processes Appl. 127, No. 9, 3005–3013 (2017; Zbl 1372.60059); the first author and N. Juillet, Ann. Probab. 44, No. 1, 42–106 (2016; Zbl 1348.49045); L. Campi et al., Finance Stoch. 21, No. 2, 471–486 (2017; Zbl 1369.91174); P. Henry-Labordère and N. Touzi, Finance Stoch. 20, No. 3, 635–668 (2016; Zbl 1369.91181)]) and which can be viewed as a martingale analogue of the classical monotone rearrangement. As another canonical element of this family we identify a martingale coupling that resembles the usual product coupling and appears as an optimizer in the general transport problem recently introduced by N. Gozlan et al. [J. Funct. Anal. 273, No. 11, 3327–3405 (2017; Zbl 1406.60032)]. In addition, this coupling provides an explicit example of a Lipschitz kernel, shedding new light on Kellerer’s proof of the existence of Markov martingales with specified marginals.