diff --git a/examples/ExternalPointMass/run.sh b/examples/ExternalPointMass/run.sh
index 9f90ca395a5c8cf83e67928b3fdbd4d8529ac254..4ac513f09cb8ac8dcefc256a68478e215b8bc320 100755
--- a/examples/ExternalPointMass/run.sh
+++ b/examples/ExternalPointMass/run.sh
@@ -7,4 +7,4 @@ then
     python makeIC.py 10000
 fi
 
-../swift -g -t 2 externalPointMass.yml 2>&1 | tee output.log
+../swift -g -t 1 externalPointMass.yml 2>&1 | tee output.log
diff --git a/src/cell.c b/src/cell.c
index 678d12dd7708960803d225e1bf2fff12e6cab7bd..d6a891aad404685a097f955503bc59615127ae40 100644
--- a/src/cell.c
+++ b/src/cell.c
@@ -854,8 +854,6 @@ void cell_set_super(struct cell *c, struct cell *super) {
   /* Set the super-cell */
   c->super = super;
 
-  //if (c->nr_tasks == 0 && super == NULL) message("No tasks here");
-
   /* Recurse */
   if (c->split)
     for (int k = 0; k < 8; k++)
diff --git a/src/const.h b/src/const.h
index afad73211546cf81cbb0e6a1179569e588952fec..43215e273d85456df66ec87720d63cfd90e11305 100644
--- a/src/const.h
+++ b/src/const.h
@@ -91,8 +91,8 @@
 #define const_gravity_eta 0.025f
 
 /* External gravity properties */
-#define EXTERNAL_POTENTIAL_NONE
-//#define EXTERNAL_POTENTIAL_POINTMASS
+//#define EXTERNAL_POTENTIAL_NONE
+#define EXTERNAL_POTENTIAL_POINTMASS
 //#define EXTERNAL_POTENTIAL_ISOTHERMALPOTENTIAL
 //#define EXTERNAL_POTENTIAL_DISC_PATCH
 
@@ -103,6 +103,6 @@
 //#define COOLING_GRACKLE
 
 /* Are we debugging ? */
-//#define SWIFT_DEBUG_CHECKS
+#define SWIFT_DEBUG_CHECKS
 
 #endif /* SWIFT_CONST_H */
diff --git a/src/engine.c b/src/engine.c
index 8e7b68fb5749bc97de4d997a86b8a135c4d3668b..7c3497b58b1d2e9d6e3918489b4a5278d1a455bb 100644
--- a/src/engine.c
+++ b/src/engine.c
@@ -110,72 +110,14 @@ void engine_addlink(struct engine *e, struct link **l, struct task *t) {
   res->next = atomic_swap(l, res);
 }
 
-/**
- * @brief Generate the gravity hierarchical tasks for a hierarchy of cells -
- * i.e. all the O(Npart) tasks.
- *
- * Tasks are only created here. The dependencies will be added later on.
- *
- * @param e The #engine.
- * @param c The #cell.
- * @param gsuper The gsuper #cell.
- */
-/* void engine_make_gravity_hierarchical_tasks(struct engine *e, struct cell *c)
- * { */
-
-/*   struct scheduler *s = &e->sched; */
-/*   const int is_with_external_gravity = */
-/*       (e->policy & engine_policy_external_gravity); */
-/*   const int is_fixdt = (e->policy & engine_policy_fixdt); */
-
-/*   /\* Are we in a cell with self/pair tasks ? *\/ */
-/*   if (c->super == c) { */
-
-/*     /\* Local tasks only... *\/ */
-/*     if (c->nodeID == e->nodeID) { */
-
-/*       /\* Add the init task. *\/ */
-/*       if (c->init == NULL) */
-/*         c->init = scheduler_addtask(s, task_type_init, task_subtype_none, 0,
- * 0, */
-/*                                     c, NULL, 0); */
-
-/*       /\* Add the kick task that matches the policy. *\/ */
-/*       if (is_fixdt) { */
-/*         if (c->kick == NULL) */
-/*           c->kick = scheduler_addtask(s, task_type_kick_fixdt, */
-/*                                       task_subtype_none, 0, 0, c, NULL, 0);
- */
-/*       } else { */
-/*         if (c->kick == NULL) */
-/*           c->kick = scheduler_addtask(s, task_type_kick, task_subtype_none,
- * 0, */
-/*                                       0, c, NULL, 0); */
-/*       } */
-
-/*       /\* External gravity task *\/ */
-/*       if (is_with_external_gravity && c->grav_external == NULL) */
-/*         c->grav_external = scheduler_addtask( */
-/*             s, task_type_grav_external, task_subtype_none, 0, 0, c, NULL, 0);
- */
-/*     } */
-
-/*   } else { */
-
-/*     /\* Recurse. *\/ */
-/*     if (c->split) */
-/*       for (int k = 0; k < 8; k++) */
-/* 	if (c->progeny[k] != NULL) */
-/* 	  engine_make_gravity_hierarchical_tasks(e, c->progeny[k]); */
-/*   } */
-/* } */
-
 /**
  * @brief Generate the hydro hierarchical tasks for a hierarchy of cells -
  * i.e. all the O(Npart) tasks.
  *
  * Tasks are only created here. The dependencies will be added later on.
  *
+ * Note that there is no need to recurse below the super-cell.
+ *
  * @param e The #engine.
  * @param c The #cell.
  * @param super The super #cell.
@@ -184,11 +126,10 @@ void engine_make_hierarchical_tasks(struct engine *e, struct cell *c) {
 
   struct scheduler *s = &e->sched;
   const int is_fixdt = (e->policy & engine_policy_fixdt);
+  const int is_hydro = (e->policy & engine_policy_hydro);
   const int is_with_cooling = (e->policy & engine_policy_cooling);
-  const int is_with_external_gravity =
-      (e->policy & engine_policy_external_gravity);
 
-  /* Are we in a cell with self/pair tasks ? */
+  /* Are we in a super-cell ? */
   if (c->super == c) {
 
     /* Local tasks only... */
@@ -208,27 +149,28 @@ void engine_make_hierarchical_tasks(struct engine *e, struct cell *c) {
       }
 
       /* Generate the ghost task. */
-      c->ghost = scheduler_addtask(s, task_type_ghost, task_subtype_none, 0, 0,
-                                   c, NULL, 0);
+      if (is_hydro)
+	c->ghost = scheduler_addtask(s, task_type_ghost, task_subtype_none, 0, 0,
+				     c, NULL, 0);
 
 #ifdef EXTRA_HYDRO_LOOP
       /* Generate the extra ghost task. */
-      c->extra_ghost = scheduler_addtask(s, task_type_extra_ghost,
-                                         task_subtype_none, 0, 0, c, NULL, 0);
+      if (is_hydro)
+	c->extra_ghost = scheduler_addtask(s, task_type_extra_ghost,
+					   task_subtype_none, 0, 0, c, NULL, 0);
 #endif
 
-      /* External gravity task */
-      if (is_with_external_gravity)  // && c->grav_external == NULL)
-        c->grav_external = scheduler_addtask(
-            s, task_type_grav_external, task_subtype_none, 0, 0, c, NULL, 0);
-
       /* Cooling task */
       if (is_with_cooling)
         c->cooling = scheduler_addtask(s, task_type_cooling, task_subtype_none,
                                        0, 0, c, NULL, 0);
     }
 
-  } else {
+  } else { /* We are above the super-cell so need to go deeper */
+
+#ifdef SWIFT_DEBUG_CHECKS
+    if (c->super != NULL) error("Incorrectly set super pointer");
+#endif
 
     /* Recurse. */
     if (c->split)
@@ -1283,6 +1225,30 @@ void engine_make_gravity_tasks(struct engine *e) {
   }
 }
 
+void engine_make_external_gravity_tasks(struct engine *e) {
+
+  struct space *s = e->s;
+  struct scheduler *sched = &e->sched;
+  const int nodeID = e->nodeID;
+  struct cell *cells = s->cells_top;
+  const int nr_cells = s->nr_cells;
+
+  for (int cid = 0; cid < nr_cells; ++cid) {
+
+    struct cell *ci = &cells[cid];
+
+    /* Skip cells without gravity particles */
+    if (ci->gcount == 0) continue;
+
+    /* Is that neighbour local ? */
+    if (ci->nodeID != nodeID) continue;
+
+    /* If the cells is local build a self-interaction */
+    scheduler_addtask(sched, task_type_self, task_subtype_external_grav, 0, 0,
+                      ci, NULL, 0);
+  }
+}
+
 /**
  * @brief Constructs the top-level pair tasks for the first hydro loop over
  * neighbours
@@ -1435,6 +1401,22 @@ static inline void engine_make_gravity_dependencies(struct scheduler *sched,
   scheduler_addunlock(sched, c->super->grav_up, gravity);
 }
 
+/**
+ * @brief Creates the dependency network for the external gravity tasks of a
+ * given cell.
+ *
+ * @param sched The #scheduler.
+ * @param gravity The gravity task to link.
+ * @param c The cell.
+ */
+static inline void engine_make_external_gravity_dependencies(
+    struct scheduler *sched, struct task *gravity, struct cell *c) {
+
+  /* init --> external gravity --> kick */
+  scheduler_addunlock(sched, c->super->init, gravity);
+  scheduler_addunlock(sched, gravity, c->super->kick);
+}
+
 /**
  * @brief Creates all the task dependencies for the gravity
  *
@@ -1480,13 +1462,21 @@ void engine_link_gravity_tasks(struct engine *e) {
       scheduler_addunlock(sched, t->ci->super->init, t);
     }
 
-    /* Self-interaction? */
+    /* Self-interaction for self-gravity? */
     if (t->type == task_type_self && t->subtype == task_subtype_grav) {
 
       engine_make_gravity_dependencies(sched, t, t->ci);
 
     }
 
+    /* Self-interaction for external gravity ? */
+    else if (t->type == task_type_self &&
+             t->subtype == task_subtype_external_grav) {
+
+      engine_make_external_gravity_dependencies(sched, t, t->ci);
+
+    }
+
     /* Otherwise, pair interaction? */
     else if (t->type == task_type_pair && t->subtype == task_subtype_grav) {
 
@@ -1510,6 +1500,15 @@ void engine_link_gravity_tasks(struct engine *e) {
       }
     }
 
+    /* Sub-self-interaction for external gravity ? */
+    else if (t->type == task_type_sub_self &&
+             t->subtype == task_subtype_external_grav) {
+
+      if (t->ci->nodeID == nodeID) {
+        engine_make_external_gravity_dependencies(sched, t, t->ci);
+      }
+    }
+
     /* Otherwise, sub-pair interaction? */
     else if (t->type == task_type_sub_pair && t->subtype == task_subtype_grav) {
 
@@ -1785,12 +1784,6 @@ void engine_make_extra_hydroloop_tasks(struct engine *e) {
 #endif
     }
 
-    /* External gravity tasks should depend on init and unlock the kick */
-    else if (t->type == task_type_grav_external) {
-      scheduler_addunlock(sched, t->ci->init, t);
-      scheduler_addunlock(sched, t, t->ci->kick);
-    }
-
     /* Cooling tasks should depend on kick and does not unlock anything since
      it is the last task*/
     else if (t->type == task_type_cooling) {
@@ -1859,6 +1852,12 @@ void engine_maketasks(struct engine *e) {
   /* Add the gravity mm tasks. */
   if (e->policy & engine_policy_self_gravity) engine_make_gravity_tasks(e);
 
+  /* Add the external gravity tasks. */
+  if (e->policy & engine_policy_external_gravity)
+    engine_make_external_gravity_tasks(e);
+
+  if (e->sched.nr_tasks == 0) error("No hydro or gravity tasks created.");
+
   /* Split the tasks. */
   scheduler_splittasks(sched);
 
@@ -1882,13 +1881,14 @@ void engine_maketasks(struct engine *e) {
   /* Count the number of tasks associated with each cell and
      store the density tasks in each cell, and make each sort
      depend on the sorts of its progeny. */
-  if (e->policy & engine_policy_hydro) engine_count_and_link_tasks(e);
+  engine_count_and_link_tasks(e);
 
   /* Now that the pair tasks are at the right level, set the super pointers. */
   for (int k = 0; k < nr_cells; k++) cell_set_super(&cells[k], NULL);
 
   /* Append hierarchical tasks to each cells */
-  for (int k = 0; k < nr_cells; k++) engine_make_hierarchical_tasks(e, &cells[k]);
+  for (int k = 0; k < nr_cells; k++)
+    engine_make_hierarchical_tasks(e, &cells[k]);
 
   /* Run through the tasks and make force tasks for each density task.
      Each force task depends on the cell ghosts and unlocks the kick task
@@ -1896,7 +1896,7 @@ void engine_maketasks(struct engine *e) {
   if (e->policy & engine_policy_hydro) engine_make_extra_hydroloop_tasks(e);
 
   /* Add the dependencies for the self-gravity stuff */
-  if (e->policy & engine_policy_self_gravity) engine_link_gravity_tasks(e);
+  engine_link_gravity_tasks(e);
 
 #ifdef WITH_MPI
 
@@ -2636,7 +2636,10 @@ void engine_init_particles(struct engine *e, int flag_entropy_ICs) {
   /* Add the tasks corresponding to external gravity to the masks */
   if (e->policy & engine_policy_external_gravity) {
 
-    mask |= 1 << task_type_grav_external;
+    mask |= 1 << task_type_self;
+    mask |= 1 << task_type_sub_self;
+
+    submask |= 1 << task_subtype_external_grav;
   }
 
   /* Add MPI tasks if need be */
@@ -2805,7 +2808,11 @@ void engine_step(struct engine *e) {
 
   /* Add the tasks corresponding to external gravity to the masks */
   if (e->policy & engine_policy_external_gravity) {
-    mask |= 1 << task_type_grav_external;
+
+    mask |= 1 << task_type_self;
+    mask |= 1 << task_type_sub_self;
+
+    submask |= 1 << task_subtype_external_grav;
   }
 
   /* Add the tasks corresponding to cooling to the masks */
diff --git a/src/runner.c b/src/runner.c
index 0a08bb5abf9af25aea889e3c9279eacb0271f388..fe81947a49194398682f621b0acefaa6ad249572 100644
--- a/src/runner.c
+++ b/src/runner.c
@@ -147,12 +147,12 @@ void runner_do_grav_external(struct runner *r, struct cell *c, int timer) {
   for (int i = 0; i < gcount; i++) {
 
     /* Get a direct pointer on the part. */
-    struct gpart *restrict g = &gparts[i];
+    struct gpart *restrict gp = &gparts[i];
 
     /* Is this part within the time step? */
-    if (g->ti_end <= ti_current) {
+    if (gp->ti_end <= ti_current) {
 
-      external_gravity_acceleration(time, potential, constants, g);
+      external_gravity_acceleration(time, potential, constants, gp);
     }
   }
 
@@ -1243,9 +1243,12 @@ void *runner_main(void *data) {
             runner_doself2_force(r, ci);
           else if (t->subtype == task_subtype_grav)
             runner_doself_grav(r, ci, 1);
+          else if (t->subtype == task_subtype_external_grav)
+            runner_do_grav_external(r, ci, 1);
           else
             error("Unknown task subtype.");
           break;
+
         case task_type_pair:
           if (t->subtype == task_subtype_density)
             runner_dopair1_density(r, ci, cj);
@@ -1260,9 +1263,7 @@ void *runner_main(void *data) {
           else
             error("Unknown task subtype.");
           break;
-        case task_type_sort:
-          runner_do_sort(r, ci, t->flags, 1);
-          break;
+
         case task_type_sub_self:
           if (t->subtype == task_subtype_density)
             runner_dosub_self1_density(r, ci, 1);
@@ -1274,9 +1275,12 @@ void *runner_main(void *data) {
             runner_dosub_self2_force(r, ci, 1);
           else if (t->subtype == task_subtype_grav)
             runner_dosub_grav(r, ci, cj, 1);
+          else if (t->subtype == task_subtype_external_grav)
+            runner_do_grav_external(r, ci, 1);
           else
             error("Unknown task subtype.");
           break;
+
         case task_type_sub_pair:
           if (t->subtype == task_subtype_density)
             runner_dosub_pair1_density(r, ci, cj, t->flags, 1);
@@ -1291,6 +1295,10 @@ void *runner_main(void *data) {
           else
             error("Unknown task subtype.");
           break;
+
+        case task_type_sort:
+          runner_do_sort(r, ci, t->flags, 1);
+          break;
         case task_type_init:
           runner_do_init(r, ci, 1);
           break;
@@ -1334,9 +1342,6 @@ void *runner_main(void *data) {
         case task_type_grav_fft:
           runner_do_grav_fft(r);
           break;
-        case task_type_grav_external:
-          runner_do_grav_external(r, t->ci, 1);
-          break;
         case task_type_cooling:
           runner_do_cooling(r, t->ci, 1);
           break;
diff --git a/src/task.c b/src/task.c
index 8da526f57886fa68121061c8eae2316912e73a30..30e90f90a420a2efc742ec2c8d8454bf01d42e86 100644
--- a/src/task.c
+++ b/src/task.c
@@ -48,13 +48,12 @@
 
 /* Task type names. */
 const char *taskID_names[task_type_count] = {
-    "none",       "sort",    "self",          "pair",          "sub_self",
-    "sub_pair",   "init",    "ghost",         "extra_ghost",   "kick",
-    "kick_fixdt", "send",    "recv",          "grav_gather_m", "grav_fft",
-    "grav_mm",    "grav_up", "grav_external", "cooling"};
+    "none", "sort",          "self",        "pair",    "sub_self",   "sub_pair",
+    "init", "ghost",         "extra_ghost", "kick",    "kick_fixdt", "send",
+    "recv", "grav_gather_m", "grav_fft",    "grav_mm", "grav_up",    "cooling"};
 
 const char *subtaskID_names[task_subtype_count] = {
-    "none", "density", "gradient", "force", "grav", "tend"};
+    "none", "density", "gradient", "force", "grav", "external_grav", "tend"};
 
 /**
  * @brief Computes the overlap between the parts array of two given cells.
@@ -134,6 +133,7 @@ __attribute__((always_inline)) INLINE static enum task_actions task_acts_on(
           break;
 
         case task_subtype_grav:
+        case task_subtype_external_grav:
           return task_action_gpart;
           break;
 
@@ -149,7 +149,14 @@ __attribute__((always_inline)) INLINE static enum task_actions task_acts_on(
     case task_type_kick_fixdt:
     case task_type_send:
     case task_type_recv:
-      return task_action_all;
+      if (t->ci->count > 0 && t->ci->gcount > 0)
+        return task_action_all;
+      else if (t->ci->count > 0)
+        return task_action_part;
+      else if (t->ci->gcount > 0)
+        return task_action_gpart;
+      else
+        error("Task without particles");
       break;
 
     case task_type_grav_gather_m:
@@ -159,10 +166,6 @@ __attribute__((always_inline)) INLINE static enum task_actions task_acts_on(
       return task_action_multipole;
       break;
 
-    case task_type_grav_external:
-      return task_action_gpart;
-      break;
-
     default:
       error("Unknown task_action for task");
       return task_action_none;
@@ -392,3 +395,15 @@ void task_print_submask(unsigned int submask) {
     printf(" %s=%s", subtaskID_names[k], (submask & (1 << k)) ? "yes" : "no");
   printf(" ]\n");
 }
+
+/**
+ * @brief Print basic information about a task.
+ *
+ * @param t The #task.
+ */
+void task_print(const struct task *t) {
+
+  message("Type:'%s' sub_type:'%s' wait=%d nr_unlocks=%d skip=%d",
+          taskID_names[t->type], subtaskID_names[t->subtype], t->wait,
+          t->nr_unlock_tasks, t->skip);
+}
diff --git a/src/task.h b/src/task.h
index 4928dc00bcd7958efdd6987b5aec90ab4b3e92fa..efd3596144cc741bb84597cdfbecd402ba02bc33 100644
--- a/src/task.h
+++ b/src/task.h
@@ -53,7 +53,6 @@ enum task_types {
   task_type_grav_fft,
   task_type_grav_mm,
   task_type_grav_up,
-  task_type_grav_external,
   task_type_cooling,
   task_type_count
 } __attribute__((packed));
@@ -67,6 +66,7 @@ enum task_subtypes {
   task_subtype_gradient,
   task_subtype_force,
   task_subtype_grav,
+  task_subtype_external_grav,
   task_subtype_tend,
   task_subtype_count
 } __attribute__((packed));
@@ -159,5 +159,6 @@ int task_lock(struct task *t);
 void task_print_mask(unsigned int mask);
 void task_print_submask(unsigned int submask);
 void task_do_rewait(struct task *t);
+void task_print(const struct task *t);
 
 #endif /* SWIFT_TASK_H */