diff --git a/changes/ticket25927.1 b/changes/ticket25927.1
new file mode 100644
index 0000000000..84ac86e187
--- /dev/null
+++ b/changes/ticket25927.1
@@ -0,0 +1,6 @@
+  o Minor features (timekeeping, circuit scheduling):
+    - When keeping track of how busy each circuit have been recently on
+      a given connection, use coarse-grained monotonic timers rather than
+      gettimeofday(). This change should marginally increase accuracy
+      and performance.  Implements part of ticket 25927.
+
diff --git a/changes/ticket25927.2 b/changes/ticket25927.2
new file mode 100644
index 0000000000..9acb4aaf6f
--- /dev/null
+++ b/changes/ticket25927.2
@@ -0,0 +1,5 @@
+  o Code simplification and refactoring:
+    - Remove our previous logic for "cached gettimeofday()" -- our coarse
+      monotonic timers are fast enough for this purpose, and far less
+      error-prone. Implements part of ticket 25927.
+
diff --git a/src/common/compat_libevent.c b/src/common/compat_libevent.c
index 9936c0aac4..707efe3892 100644
--- a/src/common/compat_libevent.c
+++ b/src/common/compat_libevent.c
@@ -494,51 +494,7 @@ tor_libevent_exit_loop_after_callback(struct event_base *base)
   event_base_loopbreak(base);
 }
 
-#if defined(LIBEVENT_VERSION_NUMBER) &&         \
-  LIBEVENT_VERSION_NUMBER >= V(2,1,1) &&        \
-  !defined(TOR_UNIT_TESTS)
-void
-tor_gettimeofday_cached(struct timeval *tv)
-{
-  event_base_gettimeofday_cached(the_event_base, tv);
-}
-void
-tor_gettimeofday_cache_clear(void)
-{
-  event_base_update_cache_time(the_event_base);
-}
-#else /* !(defined(LIBEVENT_VERSION_NUMBER) &&         ...) */
-/** Cache the current hi-res time; the cache gets reset when libevent
- * calls us. */
-static struct timeval cached_time_hires = {0, 0};
-
-/** Return a fairly recent view of the current time. */
-void
-tor_gettimeofday_cached(struct timeval *tv)
-{
-  if (cached_time_hires.tv_sec == 0) {
-    tor_gettimeofday(&cached_time_hires);
-  }
-  *tv = cached_time_hires;
-}
-
-/** Reset the cached view of the current time, so that the next time we try
- * to learn it, we will get an up-to-date value. */
-void
-tor_gettimeofday_cache_clear(void)
-{
-  cached_time_hires.tv_sec = 0;
-}
-
-#ifdef TOR_UNIT_TESTS
-/** For testing: force-update the cached time to a given value. */
-void
-tor_gettimeofday_cache_set(const struct timeval *tv)
-{
-  tor_assert(tv);
-  memcpy(&cached_time_hires, tv, sizeof(*tv));
-}
-
+#if defined(TOR_UNIT_TESTS)
 /** For testing: called post-fork to make libevent reinitialize
  * kernel structures. */
 void
@@ -548,5 +504,4 @@ tor_libevent_postfork(void)
   tor_assert(r == 0);
 }
 #endif /* defined(TOR_UNIT_TESTS) */
-#endif /* defined(LIBEVENT_VERSION_NUMBER) &&         ... */
 
diff --git a/src/common/compat_libevent.h b/src/common/compat_libevent.h
index 29c6ad375a..e2747860a9 100644
--- a/src/common/compat_libevent.h
+++ b/src/common/compat_libevent.h
@@ -68,10 +68,7 @@ void tor_libevent_free_all(void);
 
 int tor_init_libevent_rng(void);
 
-void tor_gettimeofday_cached(struct timeval *tv);
-void tor_gettimeofday_cache_clear(void);
 #ifdef TOR_UNIT_TESTS
-void tor_gettimeofday_cache_set(const struct timeval *tv);
 void tor_libevent_postfork(void);
 #endif
 
diff --git a/src/common/compat_time.c b/src/common/compat_time.c
index 966216768f..b3723f533c 100644
--- a/src/common/compat_time.c
+++ b/src/common/compat_time.c
@@ -279,6 +279,7 @@ monotime_reset_ratchets_for_testing(void)
  * nanoseconds.
  */
 static struct mach_timebase_info mach_time_info;
+static struct mach_timebase_info mach_time_info_msec_cvt;
 static int monotime_shift = 0;
 
 static void
@@ -296,6 +297,14 @@ monotime_init_internal(void)
     // requires that tor_log2(0) == 0.
     monotime_shift = tor_log2(ms_per_tick);
   }
+  {
+    // For converting ticks to milliseconds in a 32-bit-friendly way, we
+    // will first right-shift by 20, and then multiply by 20/19, since
+    // (1<<20) * 19/20 is about 1e6.  We precompute a new numerate and
+    // denominator here to avoid multiple multiplies.
+    mach_time_info_msec_cvt.numer = mach_time_info.numer * 20;
+    mach_time_info_msec_cvt.denom = mach_time_info.denom * 19;
+  }
 }
 
 /**
@@ -345,6 +354,22 @@ monotime_diff_nsec(const monotime_t *start,
   return diff_nsec;
 }
 
+int32_t
+monotime_coarse_diff_msec32_(const monotime_coarse_t *start,
+                             const monotime_coarse_t *end)
+{
+  if (BUG(mach_time_info.denom == 0)) {
+    monotime_init();
+  }
+  const int64_t diff_ticks = end->abstime_ - start->abstime_;
+
+  /* We already require in di_ops.c that right-shift performs a sign-extend. */
+  const int32_t diff_microticks = (int32_t)(diff_ticks >> 20);
+
+  return (diff_microticks * mach_time_info_msec_cvt.numer) /
+    mach_time_info_msec_cvt.denom;
+}
+
 uint32_t
 monotime_coarse_to_stamp(const monotime_coarse_t *t)
 {
@@ -443,6 +468,15 @@ monotime_diff_nsec(const monotime_t *start,
   return diff_nsec;
 }
 
+int32_t
+monotime_coarse_diff_msec32_(const monotime_coarse_t *start,
+                             const monotime_coarse_t *end)
+{
+  const int32_t diff_sec = (int32_t)(end->ts_.tv_sec - start->ts_.tv_sec);
+  const int32_t diff_nsec = (int32_t)(end->ts_.tv_nsec - start->ts_.tv_nsec);
+  return diff_sec * 1000 + diff_nsec / ONE_MILLION;
+}
+
 /* This value is ONE_BILLION >> 20. */
 static const uint32_t STAMP_TICKS_PER_SECOND = 953;
 
@@ -592,6 +626,13 @@ monotime_coarse_diff_msec(const monotime_coarse_t *start,
   return diff_ticks;
 }
 
+int32_t
+monotime_coarse_diff_msec32_(const monotime_coarse_t *start,
+                             const monotime_coarse_t *end)
+{
+  return (int32_t)monotime_coarse_diff_msec(start, end)
+}
+
 int64_t
 monotime_coarse_diff_usec(const monotime_coarse_t *start,
                           const monotime_coarse_t *end)
@@ -677,6 +718,15 @@ monotime_diff_nsec(const monotime_t *start,
   return (diff.tv_sec * ONE_BILLION + diff.tv_usec * 1000);
 }
 
+int32_t
+monotime_coarse_diff_msec32_(const monotime_coarse_t *start,
+                             const monotime_coarse_t *end)
+{
+  struct timeval diff;
+  timersub(&end->tv_, &start->tv_, &diff);
+  return diff.tv_sec * 1000 + diff.tv_usec / 1000;
+}
+
 /* This value is ONE_MILLION >> 10. */
 static const uint32_t STAMP_TICKS_PER_SECOND = 976;
 
diff --git a/src/common/compat_time.h b/src/common/compat_time.h
index 09dd6add3d..57ab20ab11 100644
--- a/src/common/compat_time.h
+++ b/src/common/compat_time.h
@@ -173,6 +173,33 @@ void monotime_coarse_add_msec(monotime_coarse_t *out,
 #define monotime_coarse_add_msec monotime_add_msec
 #endif /* defined(MONOTIME_COARSE_TYPE_IS_DIFFERENT) */
 
+/**
+ * As monotime_coarse_diff_msec, but avoid 64-bit division.
+ *
+ * Requires that the difference fit into an int32_t; not for use with
+ * large time differences.
+ */
+int32_t monotime_coarse_diff_msec32_(const monotime_coarse_t *start,
+                                     const monotime_coarse_t *end);
+
+/**
+ * As monotime_coarse_diff_msec, but avoid 64-bit division if it is expensive.
+ *
+ * Requires that the difference fit into an int32_t; not for use with
+ * large time differences.
+ */
+static inline int32_t
+monotime_coarse_diff_msec32(const monotime_coarse_t *start,
+                            const monotime_coarse_t *end)
+{
+#if SIZEOF_VOID_P == 8
+  // on a 64-bit platform, let's assume 64/64 division is cheap.
+  return (int32_t) monotime_coarse_diff_msec(start, end);
+#else
+  return monotime_coarse_diff_msec32_(start, end);
+#endif
+}
+
 MOCK_DECL(void, tor_gettimeofday, (struct timeval *timeval));
 
 #ifdef TOR_UNIT_TESTS
diff --git a/src/or/circuitmux_ewma.c b/src/or/circuitmux_ewma.c
index 4b80124a77..a360327f8e 100644
--- a/src/or/circuitmux_ewma.c
+++ b/src/or/circuitmux_ewma.c
@@ -28,7 +28,7 @@
  *
  **/
 
-#define TOR_CIRCUITMUX_EWMA_C_
+#define CIRCUITMUX_EWMA_PRIVATE
 
 #include "orconfig.h"
 
@@ -169,8 +169,6 @@ TO_EWMA_POL_CIRC_DATA(circuitmux_policy_circ_data_t *pol)
 
 static void add_cell_ewma(ewma_policy_data_t *pol, cell_ewma_t *ewma);
 static int compare_cell_ewma_counts(const void *p1, const void *p2);
-static unsigned cell_ewma_tick_from_timeval(const struct timeval *now,
-                                            double *remainder_out);
 static circuit_t * cell_ewma_to_circuit(cell_ewma_t *ewma);
 static inline double get_scale_factor(unsigned from_tick, unsigned to_tick);
 static cell_ewma_t * pop_first_cell_ewma(ewma_policy_data_t *pol);
@@ -239,6 +237,13 @@ circuitmux_policy_t ewma_policy = {
   /*.cmp_cmux =*/ ewma_cmp_cmux
 };
 
+/** Have we initialized the ewma tick-counting logic? */
+static int ewma_ticks_initialized = 0;
+/** At what monotime_coarse_t did the current tick begin? */
+static monotime_coarse_t start_of_current_tick;
+/** What is the number of the current tick? */
+static unsigned current_tick_num;
+
 /*** EWMA method implementations using the below EWMA helper functions ***/
 
 /** Compute and return the current cell_ewma tick. */
@@ -421,8 +426,6 @@ ewma_notify_xmit_cells(circuitmux_t *cmux,
   ewma_policy_circ_data_t *cdata = NULL;
   unsigned int tick;
   double fractional_tick, ewma_increment;
-  /* The current (hi-res) time */
-  struct timeval now_hires;
   cell_ewma_t *cell_ewma, *tmp;
 
   tor_assert(cmux);
@@ -435,8 +438,7 @@ ewma_notify_xmit_cells(circuitmux_t *cmux,
   cdata = TO_EWMA_POL_CIRC_DATA(pol_circ_data);
 
   /* Rescale the EWMAs if needed */
-  tor_gettimeofday_cached(&now_hires);
-  tick = cell_ewma_tick_from_timeval(&now_hires, &fractional_tick);
+  tick = cell_ewma_get_current_tick_and_fraction(&fractional_tick);
 
   if (tick != pol->active_circuit_pqueue_last_recalibrated) {
     scale_active_circuits(pol, tick);
@@ -597,24 +599,45 @@ cell_ewma_to_circuit(cell_ewma_t *ewma)
    rescale.
  */
 
-/** Given a timeval <b>now</b>, compute the cell_ewma tick in which it occurs
- * and the fraction of the tick that has elapsed between the start of the tick
- * and <b>now</b>.  Return the former and store the latter in
- * *<b>remainder_out</b>.
+/**
+ * Initialize the system that tells which ewma tick we are in.
+ */
+STATIC void
+cell_ewma_initialize_ticks(void)
+{
+  if (ewma_ticks_initialized)
+    return;
+  monotime_coarse_get(&start_of_current_tick);
+  crypto_rand((char*)&current_tick_num, sizeof(current_tick_num));
+  ewma_ticks_initialized = 1;
+}
+
+/** Compute the current cell_ewma tick and the fraction of the tick that has
+ * elapsed between the start of the tick and the current time.  Return the
+ * former and store the latter in *<b>remainder_out</b>.
  *
  * These tick values are not meant to be shared between Tor instances, or used
  * for other purposes. */
-
-static unsigned
-cell_ewma_tick_from_timeval(const struct timeval *now,
-                            double *remainder_out)
+STATIC unsigned
+cell_ewma_get_current_tick_and_fraction(double *remainder_out)
 {
-  unsigned res = (unsigned) (now->tv_sec / EWMA_TICK_LEN);
-  /* rem */
-  double rem = (now->tv_sec % EWMA_TICK_LEN) +
-    ((double)(now->tv_usec)) / 1.0e6;
-  *remainder_out = rem / EWMA_TICK_LEN;
-  return res;
+  if (BUG(!ewma_ticks_initialized)) {
+    cell_ewma_initialize_ticks(); // LCOV_EXCL_LINE
+  }
+  monotime_coarse_t now;
+  monotime_coarse_get(&now);
+  int32_t msec_diff = monotime_coarse_diff_msec32(&start_of_current_tick,
+                                                  &now);
+  if (msec_diff > (1000*EWMA_TICK_LEN)) {
+    unsigned ticks_difference = msec_diff / (1000*EWMA_TICK_LEN);
+    monotime_coarse_add_msec(&start_of_current_tick,
+                             &start_of_current_tick,
+                             ticks_difference * 1000 * EWMA_TICK_LEN);
+    current_tick_num += ticks_difference;
+    msec_diff %= 1000*EWMA_TICK_LEN;
+  }
+  *remainder_out = ((double)msec_diff) / (1.0e3 * EWMA_TICK_LEN);
+  return current_tick_num;
 }
 
 /* Default value for the CircuitPriorityHalflifeMsec consensus parameter in
@@ -678,6 +701,8 @@ cmux_ewma_set_options(const or_options_t *options,
   double halflife;
   const char *source;
 
+  cell_ewma_initialize_ticks();
+
   /* Both options and consensus can be NULL. This assures us to either get a
    * valid configured value or the default one. */
   halflife = get_circuit_priority_halflife(options, consensus, &source);
@@ -788,3 +813,12 @@ pop_first_cell_ewma(ewma_policy_data_t *pol)
                               offsetof(cell_ewma_t, heap_index));
 }
 
+/**
+ * Drop all resources held by circuitmux_ewma.c, and deinitialize the
+ * module. */
+void
+circuitmux_ewma_free_all(void)
+{
+  ewma_ticks_initialized = 0;
+}
+
diff --git a/src/or/circuitmux_ewma.h b/src/or/circuitmux_ewma.h
index 2ef8c2586d..f0c4c36095 100644
--- a/src/or/circuitmux_ewma.h
+++ b/src/or/circuitmux_ewma.h
@@ -19,5 +19,12 @@ extern circuitmux_policy_t ewma_policy;
 void cmux_ewma_set_options(const or_options_t *options,
                            const networkstatus_t *consensus);
 
+void circuitmux_ewma_free_all(void);
+
+#ifdef CIRCUITMUX_EWMA_PRIVATE
+STATIC unsigned cell_ewma_get_current_tick_and_fraction(double *remainder_out);
+STATIC void cell_ewma_initialize_ticks(void);
+#endif
+
 #endif /* !defined(TOR_CIRCUITMUX_EWMA_H) */
 
diff --git a/src/or/connection.c b/src/or/connection.c
index de0f0485b0..c2673ade16 100644
--- a/src/or/connection.c
+++ b/src/or/connection.c
@@ -3440,7 +3440,6 @@ connection_handle_read(connection_t *conn)
 {
   int res;
 
-  tor_gettimeofday_cache_clear();
   res = connection_handle_read_impl(conn);
   return res;
 }
@@ -3983,7 +3982,6 @@ int
 connection_handle_write(connection_t *conn, int force)
 {
     int res;
-    tor_gettimeofday_cache_clear();
     conn->in_connection_handle_write = 1;
     res = connection_handle_write_impl(conn, force);
     conn->in_connection_handle_write = 0;
diff --git a/src/or/main.c b/src/or/main.c
index c03e80dc03..cf0df9ba79 100644
--- a/src/or/main.c
+++ b/src/or/main.c
@@ -59,6 +59,7 @@
 #include "circuitbuild.h"
 #include "circuitlist.h"
 #include "circuituse.h"
+#include "circuitmux_ewma.h"
 #include "command.h"
 #include "compress.h"
 #include "config.h"
@@ -3590,6 +3591,7 @@ tor_free_all(int postfork)
   consdiffmgr_free_all();
   hs_free_all();
   dos_free_all();
+  circuitmux_ewma_free_all();
   if (!postfork) {
     config_free_all();
     or_state_free_all();
diff --git a/src/test/test_channel.c b/src/test/test_channel.c
index 812ec6c1ac..7d5018ef5b 100644
--- a/src/test/test_channel.c
+++ b/src/test/test_channel.c
@@ -544,6 +544,8 @@ test_channel_outbound_cell(void *arg)
 
   (void) arg;
 
+  cmux_ewma_set_options(NULL,NULL);
+
   /* The channel will be freed so we need to hijack this so the scheduler
    * doesn't get confused. */
   MOCK(scheduler_release_channel, scheduler_release_channel_mock);
diff --git a/src/test/test_circuitmux.c b/src/test/test_circuitmux.c
index 75b7a0ea47..14c7598703 100644
--- a/src/test/test_circuitmux.c
+++ b/src/test/test_circuitmux.c
@@ -3,6 +3,7 @@
 
 #define TOR_CHANNEL_INTERNAL_
 #define CIRCUITMUX_PRIVATE
+#define CIRCUITMUX_EWMA_PRIVATE
 #define RELAY_PRIVATE
 #include "or.h"
 #include "channel.h"
@@ -79,8 +80,47 @@ test_cmux_destroy_cell_queue(void *arg)
   tor_free(dc);
 }
 
+static void
+test_cmux_compute_ticks(void *arg)
+{
+  const int64_t NS_PER_S = 1000 * 1000 * 1000;
+  const int64_t START_NS = U64_LITERAL(1217709000)*NS_PER_S;
+  int64_t now;
+  double rem;
+  unsigned tick;
+  (void)arg;
+  circuitmux_ewma_free_all();
+  monotime_enable_test_mocking();
+
+  monotime_coarse_set_mock_time_nsec(START_NS);
+  cell_ewma_initialize_ticks();
+  const unsigned tick_zero = cell_ewma_get_current_tick_and_fraction(&rem);
+  tt_double_op(rem, OP_GT, -1e-9);
+  tt_double_op(rem, OP_LT, 1e-9);
+
+  /* 1.5 second later and we should still be in the same tick. */
+  now = START_NS + NS_PER_S + NS_PER_S/2;
+  monotime_coarse_set_mock_time_nsec(now);
+  tick = cell_ewma_get_current_tick_and_fraction(&rem);
+  tt_uint_op(tick, OP_EQ, tick_zero);
+  tt_double_op(rem, OP_GT, .149999999);
+  tt_double_op(rem, OP_LT, .150000001);
+
+  /* 25 second later and we should be in another tick. */
+  now = START_NS + NS_PER_S * 25;
+  monotime_coarse_set_mock_time_nsec(now);
+  tick = cell_ewma_get_current_tick_and_fraction(&rem);
+  tt_uint_op(tick, OP_EQ, tick_zero + 2);
+  tt_double_op(rem, OP_GT, .499999999);
+  tt_double_op(rem, OP_LT, .500000001);
+
+ done:
+  ;
+}
+
 struct testcase_t circuitmux_tests[] = {
   { "destroy_cell_queue", test_cmux_destroy_cell_queue, TT_FORK, NULL, NULL },
+  { "compute_ticks", test_cmux_compute_ticks, TT_FORK, NULL, NULL },
   END_OF_TESTCASES
 };
 
diff --git a/src/test/test_util.c b/src/test/test_util.c
index 350273bf4c..9c028fd47d 100644
--- a/src/test/test_util.c
+++ b/src/test/test_util.c
@@ -6035,6 +6035,9 @@ test_util_monotonic_time_add_msec(void *arg)
   monotime_coarse_add_msec(&ct2, &ct1, 1337);
   tt_i64_op(monotime_diff_msec(&t1, &t2), OP_EQ, 1337);
   tt_i64_op(monotime_coarse_diff_msec(&ct1, &ct2), OP_EQ, 1337);
+  // The 32-bit variant must be within 1% of the regular one.
+  tt_int_op(monotime_coarse_diff_msec32_(&ct1, &ct2), OP_GT, 1323);
+  tt_int_op(monotime_coarse_diff_msec32_(&ct1, &ct2), OP_LT, 1350);
 
   /* Add 1337 msec twice more; make sure that any second rollover issues
    * worked. */
@@ -6044,6 +6047,8 @@ test_util_monotonic_time_add_msec(void *arg)
   monotime_coarse_add_msec(&ct2, &ct2, 1337);
   tt_i64_op(monotime_diff_msec(&t1, &t2), OP_EQ, 1337*3);
   tt_i64_op(monotime_coarse_diff_msec(&ct1, &ct2), OP_EQ, 1337*3);
+  tt_int_op(monotime_coarse_diff_msec32_(&ct1, &ct2), OP_GT, 3970);
+  tt_int_op(monotime_coarse_diff_msec32_(&ct1, &ct2), OP_LT, 4051);
 
  done:
   ;