diff --git a/applications/ebos/eclproblem.hh b/applications/ebos/eclproblem.hh
index bfccc7472..1074a3bfd 100644
--- a/applications/ebos/eclproblem.hh
+++ b/applications/ebos/eclproblem.hh
@@ -683,6 +683,14 @@ public:
             rate[eqIdx] /= this->model().dofTotalVolume(globalDofIdx);
     }
 
+    /*!
+     * \brief Returns a reference to the ECL well manager used by the problem.
+     *
+     * This can be used for inspecting wells outside of the problem.
+     */
+    const EclWellManager<TypeTag>& wellManager() const
+    { return wellManager_; }
+
 private:
     static bool enableEclOutput_()
     { return EWOMS_GET_PARAM(TypeTag, bool, EnableEclOutput); }
diff --git a/applications/ebos/eclwellmanager.hh b/applications/ebos/eclwellmanager.hh
index 59d805217..27046bd64 100644
--- a/applications/ebos/eclwellmanager.hh
+++ b/applications/ebos/eclwellmanager.hh
@@ -174,7 +174,7 @@ public:
         computeWellCompletionsMap_(episodeIdx, wellCompMap);
 
         if (wasRestarted || wellTopologyChanged_(eclState, episodeIdx)) {
-            updateWellTopology_(episodeIdx, wellCompMap);
+            updateWellTopology_(episodeIdx, wellCompMap, gridDofIsPenetrated_);
         }
 
         // set those parameters of the wells which do not change the topology of the
@@ -367,6 +367,12 @@ public:
         return wellNameToIndex_.find( wellName ) != wellNameToIndex_.end();
     }
 
+    /*!
+     * \brief Returns true iff a given degree of freedom is currently penetrated by any well.
+     */
+    bool gridDofIsPenetrated(int globalDofIdx) const
+    { return gridDofIsPenetrated_[globalDofIdx]; }
+
     /*!
      * \brief Given a well name, return the corresponding index.
      *
@@ -548,8 +554,10 @@ public:
                                  int dofIdx,
                                  int timeIdx) const
     {
-        for (int eqIdx = 0; eqIdx < numEq; ++ eqIdx)
-            q[eqIdx] = 0.0;
+        q = 0.0;
+
+        if (!gridDofIsPenetrated(context.globalSpaceIndex(dofIdx, timeIdx)))
+            return;
 
         RateVector wellRate;
 
@@ -690,7 +698,9 @@ protected:
         return false;
     }
 
-    void updateWellTopology_(int reportStepIdx, const WellCompletionsMap& wellCompletions)
+    void updateWellTopology_(int reportStepIdx,
+                             const WellCompletionsMap& wellCompletions,
+                             std::vector<bool>& gridDofIsPenetrated) const
     {
         auto& model = simulator_.model();
         const auto& gridManager = simulator_.gridManager();
@@ -704,6 +714,10 @@ protected:
 
         // tell the active wells which DOFs they contain
         const auto gridView = simulator_.gridManager().gridView();
+
+        gridDofIsPenetrated.resize(model.numGridDof());
+        std::fill(gridDofIsPenetrated.begin(), gridDofIsPenetrated.end(), false);
+
         ElementContext elemCtx(simulator_);
         auto elemIt = gridView.template begin</*codim=*/0>();
         const auto elemEndIt = gridView.template end</*codim=*/0>();
@@ -723,6 +737,8 @@ protected:
                     // it...
                     continue;
 
+                gridDofIsPenetrated[globalDofIdx] = true;
+
                 auto eclWell = wellCompletions.at(cartesianDofIdx).second;
                 eclWell->addDof(elemCtx, dofIdx);
 
@@ -868,6 +884,7 @@ protected:
     Simulator &simulator_;
 
     std::vector<std::shared_ptr<Well> > wells_;
+    std::vector<bool> gridDofIsPenetrated_;
     std::map<std::string, int> wellNameToIndex_;
     std::map<std::string, std::array<Scalar, numPhases> > wellTotalInjectedVolume_;
     std::map<std::string, std::array<Scalar, numPhases> > wellTotalProducedVolume_;