Most work in causal inference considers extreme deterministic interventions where everyone's treatment is set to some fixed value. However, these interventions can lead to non-identification, inefficiency, and effects with little practical relevance; softer incremental effects offer a way forward. Here we detail recent work extending incremental effects to continuous and confounded treatments. In particular, we consider soft stochastic interventions based on exponential tilts, deriving the efficient influence function and semiparametric efficiency bound, along with minimax lower bounds illustrating a new effective sample size. We establish new convergence rates and bias bounds using mixed supremum and L2 norms, and give an estimator of the dose-response curve, with a detailed study of convergence rates in this nonparametric regime. Next we explore unmeasured confounding: crucially, standard stochastic interventions have a surprising property that bounds do not collapse even when set to the observational policy. Thus, we study generalized policies in which treatment rules can depend on not only covariates, but also the observed treatment; we show that these can resolve this non-collapsing bound issue. Drawing connections to the theory of optimal transport, we characterize generalized policies that minimize bound width in various models. These optimal policies are new and can have a more parsimonious interpretation compared to their usual stochastic policy analogues. We develop flexible, efficient, and robust estimators for the sharp nonparametric bounds that emerge from the framework.