A low-cost, high-performance magnetic field sensor for applications such as biomagnetism and nondestructive evaluation can be fabricated by integrating a superconducting quantum interference device (SQUID) and a gradiometer on a single chip. Conventionally, the gradiometric pick-up loop would have a rectangular outline divided symmetrically about the midpoint of its length so that its spatial response was also symmetrical. However, it is also possible to divide the same outline asymmetrically, maintaining the field rejection order of the gradiometer by adding an extra crossover. The spatial response of this arrangement will also be asymmetric, which may be exploited to reduce the effects of the nearby SQUID as a magnetic anomaly or to enhance the sensitivity of the device to magnetic sources at a particular distance. The techniques to calculate the crossover positions are well established. Here we outline how different designs may be evaluated theoretically and report on first experimental results for three simple designs. Several devices have been fabricated using a well established trilayer process with high yields. The measurement of the spatial response of an asymmetric first-order gradiometer shows the expected magnetometer characteristics for a magnetic dipole source in the near field and first-order gradiometric characteristics for a far-field source. The balance of the integrated gradiometer appears to be better than one part in , and the magnetic field gradient sensitivity has been measured to be .