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. Observance of a long- and short-period timer permits channel resynchronization between devices. 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.