To establish the major body axes, late Drosophila oocytes localize determinants to discrete cortical positions: bicoid mRNA to the anterior cortex, oskar mRNA to the posterior cortex, and gurken mRNA to the margin of the anterior cortex adjacent to the oocyte nucleus (the "anterodorsal corner"). These localizations depend on microtubules that are thought to be organized such that plus end-directed motors can move cargoes, like oskar, away from the anterior/lateral surfaces and hence toward the posterior pole. Likewise, minus end-directed motors may move cargoes toward anterior destinations. Contradicting this, cytoplasmic dynein, a minus-end motor, accumulates at the posterior. Here, we report that disruption of the plus-end motor kinesin I causes a shift of dynein from posterior to anterior. This provides an explanation for the dynein paradox, suggesting that dynein is moved as a cargo toward the posterior pole by kinesin-generated forces. However, other results present a new transport polarity puzzle. Disruption of kinesin I causes partial defects in anterior positioning of the nucleus and severe defects in anterodorsal localization of gurken mRNA. Kinesin may generate anterodorsal forces directly, despite the apparent preponderance of minus ends at the anterior cortex. Alternatively, kinesin I may facilitate cytoplasmic dynein-based anterodorsal forces by repositioning dynein toward microtubule plus ends.