Disclosed herein are wireless devices operable at intermediate wireless at ranges of thousands of meters, utilizing packets that include a preamble and a data payload. Devices may be such things as keypads, door latches, occupancy monitors, sprinkler controllers and other devices needing a communications link. A digital spread-spectrum frequency hopping rotation is used, wherein packet transmissions rotate through frequency sequences. A spectrum-impact-smoothed channel set is fashioned using sequences that each specify a unique preamble frequency relative to the other sequences and channels. The set is traversed as packets are transmitted, thereby distributing the focused radio-frequency emission impact of packets having long preambles over time. Traversal of the set is by way of time slots relative to a point of synchronization in a first packet. Detailed information on various example embodiments of the inventions are provided in the Detailed Description below, and the inventions are defined by the appended claims.