Citizens in many European countries urge that the welfare of farm animals should be improved. Policy-makers propose that this could, at least to some extent, be achieved through increased consumption of animal products produced under labeling schemes guaranteeing higher standards of animal welfare. Yet considerable uncertainties exist about the ability of the market to promote animal welfare. So far the consumption of most welfare-friendly products has been limited, and the impact of driving and limiting factors is poorly understood. Reviewing market studies, we identify the factors that have shaped the relatively successful market for grass milk in Denmark. We conclude that the positive drivers such as an appealing animal welfare attribute and animal welfare being bundled with other qualities are essentially the same as those operating in connection with less successful animal welfare-friendly products. It is therefore to be expected that other animal welfare-friendly food products marketed via “natural behaviors” in the farm animals will catch the interest of consumers. However, grass milk consumption has been supported by proper labeling, ready availability and low price premiums as well as multifaceted public support. This suggests that successful cases require the joint presence of a number of positive drivers as well as low consumption barriers.