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This paper presents improvements and novel additions to our recent work on end-to-end optimized hierarchical bi-directional video compression to further advance the state-of-the-art in learned video compression. As an improvement, we combine motion estimation and prediction modules and compress refined residual motion vectors for improved rate-distortion performance. As novel addition, we adapted the gain unit proposed for image compression to flexible-rate video compression in two ways: first, the gain unit enables a single encoder model to operate at multiple rate-distortion operating points; second, we exploit the gain unit to control bit allocation among intra-coded vs. bi-directionally coded frames by fine tuning corresponding models for truly flexible-rate learned video coding. Experimental results demonstrate that we obtain state-of-the-art rate-distortion performance exceeding those of all prior art in learned video coding.