My sequence, obnoxiously entitled the Mmmmmm! system, is broken down into six steps that are followed through each round of combat, as necessary. The first round of combat still starts with an initiative roll (unless one side is surprised), which is kept through the rest of combat. Each round begins with the players announcing their intended actions. The steps are as follows:
Missiles: In the Missiles step, all ballistic attacks are made (including artillery), starting with the side that has initiative. Additionally, each later phase is marked by a "Supplementary Missiles" step, according to the type of weapon (as noted above). In this way, bows fire up to six times a round, light crossbows three times, heavy crossbows twice and other weapons (like arquebuses or artillery) fire only once. The supplementary missiles step is taken immediately after resolving the main step (whether magic, mêlée etc.), and if a combatant takes part in the main step, she loses not only any supplementary missile attack from that segment, but also her next scheduled missile attack (whether supplementary or not).
Movement: There are two movement phases that are otherwise identical. Starting with the side that has initiative, combatants can move up to their full normal movement in each phase (12" for men, 24" for cavalry and so on).
Magic: I usually don't allow a spellcaster to move or make attacks in the same round she attempts a spell. Any damage from missiles disrupts the casting.
Mêlée: This step uses the standard rules from Chainmail. While you are locked in mêlée, any non-mêlée action (including supplementary missile attacks, movement, spells and so on) becomes a miscellaneous action (see below).
Miscellaneous: This step is for any remnant action that requires some degree of concentration (such as helping a wounded comrade, imbibing a potion, lighting a flask of oil and so forth). Regardless, you can only perform a single miscellaneous action per round. Whether a player can perform other actions in previous steps and still act in the miscellaneous step is at the discretion of the referee, but any damage taken in mêlée negates the ability to use the miscellaneous step.