diff --git a/common/Makefile b/common/Makefile
index 19c87ffdf..6096266cb 100644
--- a/common/Makefile
+++ b/common/Makefile
@@ -22,6 +22,7 @@ COMMON_SRC_NOGEN :=				\
 	common/decode_array.c			\
 	common/derive_basepoints.c		\
 	common/dev_disconnect.c			\
+	common/dijkstra.c			\
 	common/ecdh_hsmd.c			\
 	common/features.c			\
 	common/fee_states.c			\
diff --git a/common/dijkstra.c b/common/dijkstra.c
new file mode 100644
index 000000000..824b82e97
--- /dev/null
+++ b/common/dijkstra.c
@@ -0,0 +1,284 @@
+/* Without this, gheap is *really* slow!  Comment out for debugging. */
+#define NDEBUG
+#include <ccan/cast/cast.h>
+#include <ccan/err/err.h>
+#include <ccan/tal/str/str.h>
+#include <ccan/time/time.h>
+#include <common/dijkstra.h>
+#include <common/gossmap.h>
+#include <gheap.h>
+#include <inttypes.h>
+#include <stdio.h>
+
+/* Each node has this side-info. */
+struct dijkstra {
+	u32 distance;
+	/* Total CLTV delay */
+	u32 total_delay;
+	/* Total cost from here to destination */
+	struct amount_msat cost;
+	/* I want to use an index here, except that gheap moves things onto
+	 * a temporary on the stack and that makes things complex. */
+	/* NULL means it's been visited already. */
+	const struct gossmap_node **heapptr;
+
+	/* We could re-evaluate to determine this, but keeps it simple */
+	struct gossmap_chan *best_chan;
+};
+
+/* Because item_mover doesn't provide a ctx ptr, we need a global anyway. */
+static struct dijkstra *global_dijkstra;
+static const struct gossmap *global_map;
+
+/* Returns UINT_MAX if unreachable. */
+u32 dijkstra_distance(const struct dijkstra *dij, u32 node_idx)
+{
+	return dij[node_idx].distance;
+}
+
+/* Total CLTV delay */
+u32 dijkstra_delay(const struct dijkstra *dij, u32 node_idx)
+{
+	return dij[node_idx].total_delay;
+}
+
+/* Total cost to get here. */
+struct amount_msat dijkstra_amount(const struct dijkstra *dij, u32 node_idx)
+{
+	return dij[node_idx].cost;
+}
+
+struct gossmap_chan *dijkstra_best_chan(const struct dijkstra *dij,
+					u32 node_idx)
+{
+	return dij[node_idx].best_chan;
+}
+
+static struct dijkstra *get_dijkstra(const struct dijkstra *dij,
+				     const struct gossmap *map,
+				     const struct gossmap_node *n)
+{
+	return cast_const(struct dijkstra *, dij) + gossmap_node_idx(map, n);
+}
+
+/* We want a minheap, not a maxheap, so this is backwards! */
+static int less_comparer(const void *const ctx,
+			 const void *const a,
+			 const void *const b)
+{
+	return get_dijkstra(global_dijkstra, global_map,
+			    *(struct gossmap_node **)a)->distance
+		> get_dijkstra(global_dijkstra, global_map,
+			       *(struct gossmap_node **)b)->distance;
+}
+
+static void item_mover(void *const dst, const void *const src)
+{
+	struct gossmap_node *n = *((struct gossmap_node **)src);
+	get_dijkstra(global_dijkstra, global_map, n)->heapptr = dst;
+	*((struct gossmap_node **)dst) = n;
+}
+
+static const struct gossmap_node **mkheap(const tal_t *ctx,
+					  struct dijkstra *dij,
+					  const struct gossmap *map,
+					  const struct gossmap_node *start,
+					  struct amount_msat sent)
+{
+	const struct gossmap_node *n, **heap;
+	size_t i;
+
+	heap = tal_arr(tmpctx, const struct gossmap_node *,
+		       gossmap_num_nodes(map));
+	for (i = 1, n = gossmap_first_node(map);
+	     n;
+	     n = gossmap_next_node(map, n), i++) {
+		struct dijkstra *d = get_dijkstra(dij, map, n);
+		if (n == start) {
+			/* First entry in heap is start, distance 0 */
+			heap[0] = start;
+			d->heapptr = &heap[0];
+			d->distance = 0;
+			d->total_delay = 0;
+			d->cost = sent;
+			i--;
+		} else {
+			heap[i] = n;
+			d->heapptr = &heap[i];
+			d->distance = UINT_MAX;
+			d->cost = AMOUNT_MSAT(-1ULL);
+			d->total_delay = 0;
+		}
+	}
+	assert(i == tal_count(heap));
+	return heap;
+}
+
+/* 365.25 * 24 * 60 / 10 */
+#define BLOCKS_PER_YEAR 52596
+
+/* We price in risk as riskfactor percent per year. */
+static struct amount_msat risk_price(struct amount_msat amount,
+				     u32 riskfactor, u32 cltv_delay)
+{
+	struct amount_msat riskfee;
+
+	if (!amount_msat_scale(&riskfee, amount,
+			       riskfactor / 100.0 / BLOCKS_PER_YEAR
+			       * cltv_delay))
+		return AMOUNT_MSAT(-1ULL);
+	return riskfee;
+}
+
+/* Do Dijkstra: start in this case is the dst node. */
+const struct dijkstra *
+dijkstra_(const tal_t *ctx,
+	  const struct gossmap *map,
+	  const struct gossmap_node *start,
+	  struct amount_msat amount,
+	  double riskfactor,
+	  bool (*channel_ok)(const struct gossmap *map,
+			     const struct gossmap_chan *c,
+			     int dir,
+			     struct amount_msat amount,
+			     void *arg),
+	  bool (*path_better)(u32 old_distance,
+			      u32 new_distance,
+			      struct amount_msat old_cost,
+			      struct amount_msat new_cost,
+			      struct amount_msat old_risk,
+			      struct amount_msat new_risk,
+			      void *arg),
+	  void *arg)
+{
+	struct dijkstra *dij;
+	const struct gossmap_node **heap;
+	size_t heapsize;
+	struct gheap_ctx gheap_ctx;
+
+	/* There doesn't seem to be much difference with fanout 2-4. */
+	gheap_ctx.fanout = 2;
+	/* There seems to be a slight decrease if we alter this value. */
+	gheap_ctx.page_chunks = 1;
+	gheap_ctx.item_size = sizeof(*heap);
+	gheap_ctx.less_comparer = less_comparer;
+	gheap_ctx.less_comparer_ctx = NULL;
+	gheap_ctx.item_mover = item_mover;
+
+	dij = tal_arr(ctx, struct dijkstra, gossmap_max_node_idx(map));
+
+	/* Pay no attention to the man behind the curtain! */
+	global_map = map;
+	global_dijkstra = dij;
+
+	/* Wikipedia's article on Dijkstra is excellent:
+	 *    https://en.wikipedia.org/wiki/Dijkstra's_algorithm
+	 * (License https://creativecommons.org/licenses/by-sa/3.0/)
+	 *
+	 * So I quote here:
+	 *
+	 * 1. Mark all nodes unvisited. Create a set of all the unvisited
+	 * nodes called the unvisited set.
+	 *
+	 * 2. Assign to every node a tentative distance value: set it to zero
+	 * for our initial node and to infinity for all other nodes. Set the
+	 * initial node as current.[14]
+	 */
+	heap = mkheap(NULL, dij, map, start, amount);
+	heapsize = tal_count(heap);
+
+	/*
+	 * 3. For the current node, consider all of its unvisited neighbouds
+	 * and calculate their tentative distances through the current
+	 * node. Compare the newly calculated tentative distance to the
+	 * current assigned value and assign the smaller one. For example, if
+	 * the current node A is marked with a distance of 6, and the edge
+	 * connecting it with a neighbour B has length 2, then the distance to
+	 * B through A will be 6 + 2 = 8. If B was previously marked with a
+	 * distance greater than 8 then change it to 8. Otherwise, the current
+	 * value will be kept.
+	 *
+	 * 4. When we are done considering all of the unvisited neighbouds of
+	 * the current node, mark the current node as visited and remove it
+	 * from the unvisited set. A visited node will never be checked again.
+	 *
+	 * 5. If the destination node has been marked visited (when planning a
+	 * route between two specific nodes) or if the smallest tentative
+	 * distance among the nodes in the unvisited set is infinity (when
+	 * planning a complete travedsal; occuds when there is no connection
+	 * between the initial node and remaining unvisited nodes), then
+	 * stop. The algorithm has finished.
+	 *
+	 * 6.  Otherwise, select the unvisited node that is marked with the
+	 * smallest tentative distance, set it as the new "current node", and
+	 * go back to step 3.
+	 */
+	while (heapsize != 0) {
+		struct dijkstra *cur_d;
+		const struct gossmap_node *cur = heap[0];
+
+		cur_d = get_dijkstra(dij, map, cur);
+		assert(cur_d->heapptr == heap);
+
+		/* Finished all reachable nodes */
+		if (cur_d->distance == UINT_MAX)
+			break;
+
+		for (size_t i = 0; i < cur->num_chans; i++) {
+			struct gossmap_node *neighbor;
+			int which_half;
+			struct gossmap_chan *c;
+			struct dijkstra *d;
+			struct amount_msat cost, new_risk, old_risk;
+
+			c = gossmap_nth_chan(map, cur, i, &which_half);
+			neighbor = gossmap_nth_node(map, c, !which_half);
+
+			d = get_dijkstra(dij, map, neighbor);
+			/* Ignore if already visited. */
+			if (!d->heapptr)
+				continue;
+
+			/* We're going from neighbor to c, hence !which_half */
+			if (!channel_ok(map, c, !which_half, cur_d->cost, arg))
+				continue;
+
+			cost = cur_d->cost;
+			if (!amount_msat_add_fee(&cost,
+						 c->half[!which_half].base_fee,
+						 c->half[!which_half].proportional_fee))
+				/* Shouldn't happen! */
+				continue;
+
+			/* cltv_delay can't overflow: only 20 bits per hop. */
+			new_risk = risk_price(cost, riskfactor,
+					      cur_d->total_delay
+					      + c->half[!which_half].delay);
+
+			old_risk = risk_price(d->cost, riskfactor,
+					      d->total_delay);
+
+			if (!path_better(d->distance,
+					 cur_d->distance + 1,
+					 d->cost,
+					 cost,
+					 old_risk,
+					 new_risk,
+					 arg))
+				continue;
+
+			d->distance = cur_d->distance + 1;
+			d->total_delay = cur_d->total_delay
+				+ c->half[!which_half].delay;
+			d->cost = cost;
+			d->best_chan = c;
+			gheap_restore_heap_after_item_increase(&gheap_ctx,
+							       heap, heapsize,
+							       d->heapptr - heap);
+		}
+		gheap_pop_heap(&gheap_ctx, heap, heapsize--);
+		cur_d->heapptr = NULL;
+	}
+	tal_free(heap);
+	return dij;
+}
diff --git a/common/dijkstra.h b/common/dijkstra.h
new file mode 100644
index 000000000..b8f2c2ff8
--- /dev/null
+++ b/common/dijkstra.h
@@ -0,0 +1,61 @@
+#ifndef LIGHTNING_COMMON_DIJKSTRA_H
+#define LIGHTNING_COMMON_DIJKSTRA_H
+#include "config.h"
+#include <ccan/tal/tal.h>
+#include <ccan/typesafe_cb/typesafe_cb.h>
+#include <common/amount.h>
+
+struct gossmap;
+struct gossmap_chan;
+struct gossmap_node;
+
+/* Do Dijkstra: start in this case is the dst node. */
+const struct dijkstra *
+dijkstra_(const tal_t *ctx,
+	  const struct gossmap *gossmap,
+	  const struct gossmap_node *start,
+	  struct amount_msat amount,
+	  double riskfactor,
+	  bool (*channel_ok)(const struct gossmap *map,
+			     const struct gossmap_chan *c,
+			     int dir,
+			     struct amount_msat amount,
+			     void *arg),
+	  bool (*path_better)(u32 old_distance,
+			      u32 new_distance,
+			      struct amount_msat old_cost,
+			      struct amount_msat new_cost,
+			      struct amount_msat old_risk,
+			      struct amount_msat new_risk,
+			      void *arg),
+	  void *arg);
+
+#define dijkstra(ctx, map, start, amount, riskfactor, channel_ok,	\
+		 path_better, arg)					\
+	dijkstra_((ctx), (map), (start), (amount), (riskfactor),	\
+		  typesafe_cb_preargs(bool, void *, (channel_ok), (arg), \
+				      const struct gossmap *,		\
+				      const struct gossmap_chan *,	\
+				      int, struct amount_msat),		\
+		  typesafe_cb_preargs(bool, void *, (path_better), (arg), \
+				      u32, u32,				\
+				      struct amount_msat,		\
+				      struct amount_msat,		\
+				      struct amount_msat,		\
+				      struct amount_msat),		\
+		  (arg))
+
+/* Returns UINT_MAX if unreachable. */
+u32 dijkstra_distance(const struct dijkstra *dij, u32 node_idx);
+
+/* Total CLTV delay (0 if unreachable) */
+u32 dijkstra_delay(const struct dijkstra *dij, u32 node_idx);
+
+/* Total cost to get here (-1ULL if unreachable) */
+struct amount_msat dijkstra_amount(const struct dijkstra *dij, u32 node_idx);
+
+/* Best path we found to here */
+struct gossmap_chan *dijkstra_best_chan(const struct dijkstra *dij,
+					u32 node_idx);
+
+#endif /* LIGHTNING_COMMON_DIJKSTRA_H */