diff --git a/lmcp.lua b/lmcp.lua
index 8dc7075..90a31e5 100644
--- a/lmcp.lua
+++ b/lmcp.lua
@@ -69,6 +69,11 @@ function lmcp.new(name, opts)
     -- server calls `:roots(session_id, ...)`; invalidated when the client
     -- sends notifications/roots/list_changed.
     self._roots_cache = {}
+    -- Pending handler coroutines (issue #20 — concurrent dispatch).
+    -- Each entry: { co, conn, wake_at, finalise }. The scheduler tick
+    -- resumes any whose wake_at has passed and runs `finalise` on the
+    -- coroutine's return value to build the deferred response.
+    self._pending_handlers = {}
     -- Notification queue: drained by Streamable HTTP transport (issue #16).
     -- Today delivery is a no-op; we still enqueue so the emission code
     -- path is exercised. Capped + deduped to keep the queue useful.
@@ -887,6 +892,10 @@ end
 
 -- ---- Dispatch a fully-parsed POST body ----
 
+-- Forward declarations: used by _dispatch_post, defined below.
+local _drive_handler_co
+local _finalise_dispatch
+
 local function _dispatch_post(self, conn)
     local body = conn.body
     if body == "" then
@@ -943,27 +952,73 @@ local function _dispatch_post(self, conn)
     -- session to push the request onto).
     rpc_req._session_id = sess.id
 
-    -- Normal client request / notification. Dispatch via handle_request.
-    local response = self:handle_request(rpc_req)
-    if not response then
+    -- Concurrent handler dispatch (issue #20). Wrap the dispatch call in
+    -- a coroutine so any tool handler that goes through server.lua:run()
+    -- (which yields when polling its sentinel file) can return control to
+    -- the event loop while it waits. Other connections continue making
+    -- progress.
+    --
+    -- The coroutine resumes itself synchronously the first time. If it
+    -- completes without yielding (pure-Lua handlers, ping, etc.) the
+    -- response is built inline as before. If it yields, we park it in
+    -- self._pending_handlers and return nil — the conn enters
+    -- dispatching_async, the scheduler tick resumes when wake_at passes.
+    local co = coroutine.create(function()
+        return self:handle_request(rpc_req)
+    end)
+    return _drive_handler_co(self, conn, co)
+end
+
+-- Resume a handler coroutine until it completes or yields. On completion,
+-- build the deferred HTTP response (preserving the Accept-aware shape).
+-- On yield, register in self._pending_handlers and return nil — the conn
+-- is parked in dispatching_async until the scheduler resumes it.
+_drive_handler_co = function(self, conn, co)
+    local rok, ryield = coroutine.resume(co)
+    if coroutine.status(co) == "dead" then
+        return _finalise_dispatch(conn, rok, ryield)
+    end
+    -- Suspended. Parse the yield payload.
+    local wake_at = (type(ryield) == "table" and ryield.wake_at) or 0
+    self._pending_handlers[#self._pending_handlers + 1] = {
+        co = co, conn = conn, wake_at = wake_at,
+    }
+    conn.state = "dispatching_async"
+    return nil  -- no write_buf change; conn parks
+end
+
+-- Build the HTTP response for a completed dispatch. `rok` is the coroutine.resume
+-- success flag; `result` is the handler/dispatch return (a JSON-RPC string when
+-- rok=true; an error message when rok=false). Used by both the sync path
+-- (_dispatch_post tail) and the async resume path (_scheduler_tick).
+_finalise_dispatch = function(conn, rok, result)
+    local session_id = conn.session_id
+    if not rok then
+        -- Internal dispatch error — surface as a JSON-RPC error response.
+        return _build_http_response("500 Internal Server Error",
+            { ["Content-Type"] = "application/json",
+              ["Access-Control-Allow-Origin"] = "*" },
+            jsonrpc_error(nil, -32603, "Internal error: " .. tostring(result)),
+            session_id)
+    end
+    if not result then
         -- Notification → 202 Accepted, no body.
         return _build_http_response("202 Accepted",
             { ["Content-Type"] = "application/json",
               ["Access-Control-Allow-Origin"] = "*" },
-            "", conn.session_id)
+            "", session_id)
     end
-
-    -- If client accepts SSE, respond as a single-event SSE stream.
-    -- Otherwise plain JSON body.
+    -- Accept-aware response shape (re-checked at finalise time; survives
+    -- parking because conn.headers is captured by the closure scope).
     local accept = conn.headers["accept"] or ""
     if accept:find("text/event%-stream") then
-        local hdrs = _build_sse_headers(conn.session_id)
-        return hdrs .. _sse_event(response)
+        local hdrs = _build_sse_headers(session_id)
+        return hdrs .. _sse_event(result)
     end
     return _build_http_response("200 OK",
         { ["Content-Type"] = "application/json",
           ["Access-Control-Allow-Origin"] = "*" },
-        response, conn.session_id)
+        result, session_id)
 end
 
 local function _dispatch_options(conn)
@@ -1119,8 +1174,15 @@ local function _conn_read(self, conn)
             conn.state = "sse_open"
             conn.last_heart = os.time()
         elseif conn.method == "POST" then
-            conn.write_buf = _dispatch_post(self, conn)
-            conn.state = "writing"
+            -- _dispatch_post may return nil (issue #20) if the handler
+            -- coroutine yielded. In that case it set conn.state =
+            -- "dispatching_async" itself and parked the coroutine.
+            local resp = _dispatch_post(self, conn)
+            if resp then
+                conn.write_buf = resp
+                conn.state = "writing"
+            end
+            -- else: conn already parked; scheduler tick will finalise.
         else
             conn.write_buf = _build_http_response("405 Method Not Allowed",
                 { ["Content-Type"] = "text/plain",
@@ -1195,6 +1257,63 @@ local function _heartbeat_tick(self)
     end
 end
 
+-- Issue #20 — scheduler tick. Resume any parked dispatch coroutine whose
+-- wake_at has passed. On completion, build the deferred response and
+-- queue it for write. If the connection died while the handler was
+-- parked, drop the coroutine.
+--
+-- gettime() is wall-clock (luasocket uses gettimeofday) — NOT monotonic.
+-- A large NTP step backwards could delay resumes; forwards could bunch
+-- them. Acceptable for the deployment fleet (chrony slews); revisit if
+-- a use case appears that needs CLOCK_MONOTONIC.
+local function _scheduler_tick(self)
+    if not self._pending_handlers[1] then return end
+    local socket = require("socket")
+    local now = socket.gettime()
+    local i = 1
+    while i <= #self._pending_handlers do
+        local p = self._pending_handlers[i]
+        if p.conn.state == "closing" then
+            -- Connection died mid-handler; drop the coroutine entirely.
+            table.remove(self._pending_handlers, i)
+        elseif now >= p.wake_at then
+            -- Time to resume. Remove from pending BEFORE resume so a
+            -- re-yielding handler re-adds itself cleanly via _drive_handler_co.
+            table.remove(self._pending_handlers, i)
+            local rok, ryield = coroutine.resume(p.co)
+            if coroutine.status(p.co) == "dead" then
+                p.conn.write_buf = (p.conn.write_buf or "")
+                    .. _finalise_dispatch(p.conn, rok, ryield)
+                p.conn.state = "writing"
+            else
+                -- Yielded again — re-park.
+                local wake_at = (type(ryield) == "table" and ryield.wake_at) or 0
+                self._pending_handlers[#self._pending_handlers + 1] = {
+                    co = p.co, conn = p.conn, wake_at = wake_at,
+                }
+            end
+        else
+            i = i + 1
+        end
+    end
+end
+
+-- Returns the earliest pending wake_at as an offset from now, or nil if
+-- no handlers are parked. Used to tighten the select() timeout so the
+-- scheduler wakes on the right beat.
+local function _next_pending_delay(self)
+    if not self._pending_handlers[1] then return nil end
+    local socket = require("socket")
+    local now = socket.gettime()
+    local earliest = math.huge
+    for _, p in ipairs(self._pending_handlers) do
+        if p.wake_at < earliest then earliest = p.wake_at end
+    end
+    local d = earliest - now
+    if d < 0 then return 0 end
+    return d
+end
+
 -- ---- Public: server-initiated request (for sampling/roots/etc.) ----
 -- Enqueues a JSON-RPC request on the session's SSE stream. The callback
 -- fires when the client POSTs back the response (matched by id).
@@ -1322,7 +1441,14 @@ function lmcp:run()
             end
         end
 
-        local ready_r, ready_w = socket.select(reads, writes, SELECT_TIMEOUT)
+        -- Tighten select timeout if a parked handler is due sooner.
+        -- Otherwise a 100ms tick adds 100ms latency to short shell-tool runs.
+        local select_timeout = SELECT_TIMEOUT
+        local next_pend = _next_pending_delay(self)
+        if next_pend and next_pend < select_timeout then
+            select_timeout = next_pend
+        end
+        local ready_r, ready_w = socket.select(reads, writes, select_timeout)
 
         for _, sock in ipairs(ready_r or {}) do
             if sock == server_sock then
@@ -1365,9 +1491,11 @@ function lmcp:run()
         -- Per-tick maintenance.
         _drain_notifications(self)
         _heartbeat_tick(self)
+        _scheduler_tick(self)  -- issue #20: resume due dispatch coroutines
 
         -- After draining, attempt immediate writes on conns whose write_buf
-        -- just got bytes (so list_changed / heartbeat appears within one tick).
+        -- just got bytes (so list_changed / heartbeat / async-completed
+        -- responses appear within one tick).
         for sock, conn in pairs(self._conns) do
             if conn.write_buf ~= "" and conn.state ~= "closing" then
                 pcall(_conn_write, conn)
diff --git a/server.lua b/server.lua
index 05fa311..f4e64ef 100644
--- a/server.lua
+++ b/server.lua
@@ -35,7 +35,35 @@ local function tmpname()
     end
 end
 
+-- Lazy-required luasocket — only needed in the coroutine path for
+-- gettime(). Avoids forcing luasocket as a hard dep at server.lua
+-- load time (callers like example_server already require it via lmcp).
+local _socket = nil
+local function gettime()
+    if not _socket then _socket = require("socket") end
+    return _socket.gettime()
+end
+
+-- in_coroutine() — true if we're running inside an lmcp dispatch
+-- coroutine (issue #20). Handles both Lua 5.4 (coroutine.running →
+-- (co, isMain)) and LuaJIT 5.1 (coroutine.running → nil on main).
+local function in_coroutine()
+    local co, is_main = coroutine.running()
+    if co == nil then return false end       -- 5.1 / LuaJIT main
+    if is_main then return false end          -- 5.4 main thread
+    return true
+end
+
 local function sleep_ms(ms)
+    -- Coroutine-aware: yield with a wake deadline instead of busy-blocking.
+    -- The lmcp event loop services I/O for other connections while this
+    -- coroutine sleeps, then resumes it once the deadline elapses.
+    -- (Issue #20: gives concurrent tool dispatch without changing handler
+    -- source code — tools that go through run() get it for free.)
+    if in_coroutine() then
+        coroutine.yield({ wake_at = gettime() + (ms / 1000) })
+        return
+    end
     if WINDOWS then
         -- ping loopback: ~1s per -n count. For sub-second, use busy-wait.
         if ms < 500 then
@@ -78,6 +106,22 @@ local function run(cmd, timeout_sec)
     local out_file = base .. ".out"
     local done_file = base .. ".done"
 
+    -- Wall-clock deadline rather than an accumulated interval-counter:
+    -- when we're inside a dispatch coroutine (issue #20), the scheduler
+    -- may delay our resume by more than `interval`, so an accumulator
+    -- diverges from real elapsed. gettime() comparison stays honest in
+    -- both busy-poll and yield-resume modes.
+    local started = gettime()
+    local function poll_loop()
+        local interval = WINDOWS and 100 or 50  -- ms
+        while gettime() - started < timeout_sec do
+            if file_exists(done_file) then return true end
+            sleep_ms(interval)
+            if interval < 2000 then interval = math.floor(interval * 1.5) end
+        end
+        return false
+    end
+
     if WINDOWS then
         -- Write a batch wrapper that runs the command and signals completion
         local bat_file = base .. ".bat"
@@ -89,22 +133,13 @@ local function run(cmd, timeout_sec)
         bf:close()
         os.execute('start /B cmd /C "' .. bat_file .. '"')
 
-        -- Poll for sentinel
-        local elapsed = 0
-        local interval = 100  -- ms
-        while elapsed < timeout_sec * 1000 do
-            if file_exists(done_file) then break end
-            sleep_ms(interval)
-            elapsed = elapsed + interval
-            if interval < 2000 then interval = math.floor(interval * 1.5) end
-        end
-
+        local completed = poll_loop()
         local output = read_file(out_file)
         remove_silent(bat_file)
         remove_silent(out_file)
         remove_silent(done_file)
 
-        if elapsed >= timeout_sec * 1000 then
+        if not completed then
             return output or ("Error: command timed out after " .. timeout_sec .. "s")
         end
         return output and output ~= "" and output or "(no output)"
@@ -117,20 +152,12 @@ local function run(cmd, timeout_sec)
         )
         os.execute("sh -c '" .. sh_cmd:gsub("'", "'\\''") .. "' &")
 
-        local elapsed = 0
-        local interval = 50  -- ms
-        while elapsed < timeout_sec * 1000 do
-            if file_exists(done_file) then break end
-            sleep_ms(interval)
-            elapsed = elapsed + interval
-            if interval < 2000 then interval = math.floor(interval * 1.5) end
-        end
-
+        local completed = poll_loop()
         local output = read_file(out_file)
         remove_silent(out_file)
         remove_silent(done_file)
 
-        if elapsed >= timeout_sec * 1000 then
+        if not completed then
             return output or ("Error: command timed out after " .. timeout_sec .. "s")
         end
         return output and output ~= "" and output or "(no output)"