diff --git a/opm/input/eclipse/EclipseState/Grid/EclipseGrid.hpp b/opm/input/eclipse/EclipseState/Grid/EclipseGrid.hpp
index aadb88d0f..744c858e1 100644
--- a/opm/input/eclipse/EclipseState/Grid/EclipseGrid.hpp
+++ b/opm/input/eclipse/EclipseState/Grid/EclipseGrid.hpp
@@ -64,7 +64,8 @@ namespace Opm {
         EclipseGrid(const EclipseGrid& src, const double* zcorn, const std::vector<int>& actnum);
 
         EclipseGrid(size_t nx, size_t ny, size_t nz,
-                    double dx = 1.0, double dy = 1.0, double dz = 1.0);
+                    double dx = 1.0, double dy = 1.0, double dz = 1.0,
+                    double top = 0.0);
         explicit EclipseGrid(const GridDims& gd);
 
         EclipseGrid(const std::array<int, 3>& dims ,
diff --git a/src/opm/input/eclipse/EclipseState/Grid/EclipseGrid.cpp b/src/opm/input/eclipse/EclipseState/Grid/EclipseGrid.cpp
index f033f86c1..e1dcdd3d2 100644
--- a/src/opm/input/eclipse/EclipseState/Grid/EclipseGrid.cpp
+++ b/src/opm/input/eclipse/EclipseState/Grid/EclipseGrid.cpp
@@ -155,7 +155,7 @@ EclipseGrid::EclipseGrid(const GridDims& gd)
 
 
 EclipseGrid::EclipseGrid(size_t nx, size_t ny , size_t nz,
-                         double dx, double dy, double dz)
+                         double dx, double dy, double dz, double top)
     : GridDims(nx, ny, nz),
       m_minpvMode(MinpvMode::Inactive),
       m_pinchoutMode(PinchMode::TOPBOT),
@@ -186,8 +186,8 @@ EclipseGrid::EclipseGrid(size_t nx, size_t ny , size_t nz,
                 // top face of cell
                 int zind = i*2 + j*nx*4 + k*nx*ny*8;
 
-                double zt = k*dz;
-                double zb = (k+1)*dz;
+                double zt = top + k*dz;
+                double zb = top + (k+1)*dz;
 
                 m_zcorn[zind] = zt;
                 m_zcorn[zind + 1] = zt;
diff --git a/src/opm/input/eclipse/Schedule/MSW/Compsegs.cpp b/src/opm/input/eclipse/Schedule/MSW/Compsegs.cpp
index b12f2a695..02592d11f 100644
--- a/src/opm/input/eclipse/Schedule/MSW/Compsegs.cpp
+++ b/src/opm/input/eclipse/Schedule/MSW/Compsegs.cpp
@@ -89,9 +89,10 @@ struct Record {
         const double segment_depth = segment.depth();
         const double segment_distance = segment.totalLength();
 
-        // for top segment, no interpolation is needed
+        // Using top segment depth may lead to depths outside of the 
+        // perforated grid cell, so simply stick to grid cell center in this case
         if (segment_number == 1) {
-            center_depth = segment_depth;
+            center_depth = -1.0;
             return;
         }
 
@@ -324,9 +325,11 @@ namespace {
                 const int j = compseg.m_j;
                 const int k = compseg.m_k;
                 if (grid.get_cell(i, j, k).is_active()) {
+                    // Negative values to indicate cell depths should be used
+                    double cdepth = compseg.center_depth >= 0. ? compseg.center_depth : grid.get_cell(i, j, k).depth;
                     Connection& connection = new_connection_set.getFromIJK(i, j, k);
                     connection.updateSegment(compseg.segment_number,
-                                             compseg.center_depth,
+                                             cdepth,
                                              compseg.m_seqIndex,
                                              { compseg.m_distance_start, compseg.m_distance_end });
                 }
diff --git a/tests/parser/MultisegmentWellTests.cpp b/tests/parser/MultisegmentWellTests.cpp
index f301f80c9..150b450ef 100644
--- a/tests/parser/MultisegmentWellTests.cpp
+++ b/tests/parser/MultisegmentWellTests.cpp
@@ -60,7 +60,7 @@ BOOST_AUTO_TEST_CASE(AICDWellTest) {
     auto dir = Opm::Connection::Direction::Z;
     const auto kind = Opm::Connection::CTFKind::DeckValue;
     Opm::WellConnections connection_set(Opm::Connection::Order::TRACK, 10,10);
-    Opm::EclipseGrid grid(20,20,20);
+    Opm::EclipseGrid grid(20,20,20, 1., 1., 25.0, 2500.0);
     connection_set.add(Opm::Connection( 19, 0, 0,grid.getGlobalIndex(19,0,0), 1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 1,grid.getGlobalIndex(19,0,1), 1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 2,grid.getGlobalIndex(19,0,2), 1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
@@ -220,7 +220,7 @@ BOOST_AUTO_TEST_CASE(MultisegmentWellTest) {
     auto dir = Opm::Connection::Direction::Z;
     const auto kind = Opm::Connection::CTFKind::DeckValue;
     Opm::WellConnections connection_set(Opm::Connection::Order::TRACK, 10,10);
-    Opm::EclipseGrid grid(20,20,20);
+    Opm::EclipseGrid grid(20,20,20, 1., 1., 25.0, 2500.0);
     connection_set.add(Opm::Connection( 19, 0, 0,grid.getGlobalIndex(19,0,0), 1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 1,grid.getGlobalIndex(19,0,1), 1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 2,grid.getGlobalIndex(19,0,2), 1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
@@ -387,7 +387,7 @@ BOOST_AUTO_TEST_CASE(WrongDistanceCOMPSEGS) {
     auto dir = Opm::Connection::Direction::Z;
     const auto kind = Opm::Connection::CTFKind::DeckValue;
     Opm::WellConnections connection_set(Opm::Connection::Order::TRACK, 10,10);
-    Opm::EclipseGrid grid(20,20,20);
+    Opm::EclipseGrid grid(20,20,20, 1., 1., 25., 2500.);
     connection_set.add(Opm::Connection( 19, 0, 0, grid.getGlobalIndex(19,0,0),1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 1, grid.getGlobalIndex(19,0,1),1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 2, grid.getGlobalIndex(19,0,2),1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
@@ -456,7 +456,7 @@ BOOST_AUTO_TEST_CASE(NegativeDepthCOMPSEGS) {
     auto dir = Opm::Connection::Direction::Z;
     const auto kind = Opm::Connection::CTFKind::DeckValue;
     Opm::WellConnections connection_set(Opm::Connection::Order::TRACK, 10,10);
-    Opm::EclipseGrid grid(20,20,20);
+    Opm::EclipseGrid grid(20,20,20, 1., 1., 25., 2500.);
     connection_set.add(Opm::Connection( 19, 0, 0, grid.getGlobalIndex(19,0,0),1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 1, grid.getGlobalIndex(19,0,1),1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 2, grid.getGlobalIndex(19,0,2),1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
@@ -525,7 +525,7 @@ BOOST_AUTO_TEST_CASE(testwsegvalv) {
     auto dir = Opm::Connection::Direction::Z;
     const auto kind = Opm::Connection::CTFKind::DeckValue;
     Opm::WellConnections connection_set(Opm::Connection::Order::TRACK, 10,10);
-    Opm::EclipseGrid grid(20,20,20);
+    Opm::EclipseGrid grid(20,20,20, 1., 1., 25., 2500.);
     connection_set.add(Opm::Connection( 19, 0, 0, grid.getGlobalIndex(19,0,0), 1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 1, grid.getGlobalIndex(19,0,1), 1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );
     connection_set.add(Opm::Connection( 19, 0, 2, grid.getGlobalIndex(19,0,2), 1, 0.0, Opm::Connection::State::OPEN , 200, 17.29, 0.25, 0.0, 0.0, 0.0, 0.0, 0, dir, kind, 0, true) );