Robotic harvesters that use visual servoing must choose the best direction from which to approach the fruit to minimize occlusion and avoid obstacles that might interfere with the detection along the approach. This work proposes different approach strategies, compares them in terms of cycle times, and presents a failure analysis methodology of the different approach strategies. The different approach strategies are: in-field assessment by human observers, evaluation based on an overview image using advanced algorithms or remote human observers, or attempting multiple approach directions until the fruit is successfully reached. In the latter approach, each attempt costs time, which is a major bottleneck in bringing harvesting robots into the market. Alternatively, a single approach strategy that only attempts one direction can be applied if the best approach direction is known a-priori. The different approach strategies were evaluated for a case study of sweet pepper harvesting in laboratorial and greenhouse conditions. The first experiment, conducted in a commercial greenhouse, revealed that the fruit approach cycle time increased 8% and 116% for reachable and unreachable fruits respectively when the multiple approach strategy was applied, compared to the single approach strategy. The second experiment measured human observers’ ability to provide insights to approach directions based on overview images taken in both greenhouse and laboratorial conditions. Results revealed that human observers are accurate in detecting unapproachable directions while they tend to miss approachable directions. By detecting fruits that are unreachable (via automatic algorithms or human operators), harvesting cycle times can be significantly shortened leading to improved commercial feasibility of harvesting robots.