Recent progress in robotic manipulation has dealt with the case of previously\nunknown objects in the context of relatively simple tasks, such as bin-picking.\nExisting methods for more constrained problems, however, such as deliberate\nplacement in a tight region, depend more critically on shape information to\nachieve safe execution. This work deals with pick-and-constrained placement of\nobjects without access to geometric models. The objective is to pick an object\nand place it safely inside a desired goal region without any collisions, while\nminimizing the time and the sensing operations required to complete the task.\nAn algorithmic framework is proposed for this purpose, which performs\nmanipulation planning simultaneously over a conservative and an optimistic\nestimate of the object's volume. The conservative estimate ensures that the\nmanipulation is safe while the optimistic estimate guides the sensor-based\nmanipulation process when no solution can be found for the conservative\nestimate. To maintain these estimates and dynamically update them during\nmanipulation, objects are represented by a simple volumetric representation,\nwhich stores sets of occupied and unseen voxels. The effectiveness of the\nproposed approach is demonstrated by developing a robotic system that picks a\npreviously unseen object from a table-top and places it in a constrained space.\nThe system comprises of a dual-arm manipulator with heterogeneous end-effectors\nand leverages hand-offs as a re-grasping strategy. Real-world experiments show\nthat straightforward pick-sense-and-place alternatives frequently fail to solve\npick-and-constrained placement problems. The proposed pipeline, however,\nachieves more than 95% success rate and faster execution times as evaluated\nover multiple physical experiments.\n