diff --git a/opm/io/eclipse/rst/segment.hpp b/opm/io/eclipse/rst/segment.hpp
index 5ddcfd3b9..ba827b668 100644
--- a/opm/io/eclipse/rst/segment.hpp
+++ b/opm/io/eclipse/rst/segment.hpp
@@ -30,7 +30,7 @@ class UnitSystem;
 namespace RestartIO {
 
 struct RstSegment {
-    RstSegment(const ::Opm::UnitSystem& unit_system, const int* iseg, const double * rseg);
+    RstSegment(const ::Opm::UnitSystem& unit_system, int segment_number, const int* iseg, const double * rseg);
 
     int segment;
     int outlet_segment;
diff --git a/src/opm/io/eclipse/rst/segment.cpp b/src/opm/io/eclipse/rst/segment.cpp
index 0f995319f..cf70677f2 100644
--- a/src/opm/io/eclipse/rst/segment.cpp
+++ b/src/opm/io/eclipse/rst/segment.cpp
@@ -50,8 +50,8 @@ double area_to_si(const UnitSystem& unit_system, double raw_value) {
 }
 
 
-RstSegment::RstSegment(const ::Opm::UnitSystem& unit_system, const int * iseg, const double * rseg) :
-    segment(                                                    iseg[VI::ISeg::SegNo]),
+RstSegment::RstSegment(const ::Opm::UnitSystem& unit_system, int segment_number, const int * iseg, const double * rseg) :
+    segment(                                                    segment_number),
     outlet_segment(                                             iseg[VI::ISeg::OutSeg]),
     branch(                                                     iseg[VI::ISeg::BranchNo]),
     segment_type(                                               from_ecl<Segment::SegmentType>(iseg[VI::ISeg::SegmentType])),
diff --git a/src/opm/io/eclipse/rst/well.cpp b/src/opm/io/eclipse/rst/well.cpp
index fbf87d845..5837f9145 100644
--- a/src/opm/io/eclipse/rst/well.cpp
+++ b/src/opm/io/eclipse/rst/well.cpp
@@ -135,10 +135,11 @@ RstWell::RstWell(const ::Opm::UnitSystem& unit_system,
         for (int is=0; is < header.nsegmx; is++) {
             std::size_t iseg_offset = header.nisegz * (is + (this->msw_index - 1) * header.nsegmx);
             std::size_t rseg_offset = header.nrsegz * (is + (this->msw_index - 1) * header.nsegmx);
-            auto segment_number = iseg[iseg_offset + VI::ISeg::SegNo];
-            if (segment_number != 0) {
+            auto other_segment_number = iseg[iseg_offset + VI::ISeg::SegNo];
+            if (other_segment_number != 0) {
+                auto segment_number = is + 1;
                 segment_map.insert({segment_number, this->segments.size()});
-                this->segments.emplace_back( unit_system, iseg.data() + iseg_offset, rseg.data() + rseg_offset);
+                this->segments.emplace_back( unit_system, segment_number, iseg.data() + iseg_offset, rseg.data() + rseg_offset);
             }
         }
 
diff --git a/src/opm/parser/eclipse/EclipseState/Schedule/Schedule.cpp b/src/opm/parser/eclipse/EclipseState/Schedule/Schedule.cpp
index ddffd7f84..7de5e26d0 100644
--- a/src/opm/parser/eclipse/EclipseState/Schedule/Schedule.cpp
+++ b/src/opm/parser/eclipse/EclipseState/Schedule/Schedule.cpp
@@ -2985,9 +2985,19 @@ void Schedule::load_rst(const RestartIO::RstState& rst_state, const EclipseGrid&
 
         if (!segments.empty()) {
             std::vector<Segment> segments_list;
+            /*
+              The ordering of the segments in the WellSegments structure seems a
+              bit random; in some parts of the code the segment_number seems to
+              be treated like a random integer ID, whereas in other parts it
+              seems to be treated like a running index. Here the segments in
+              WellSegments are sorted according to the segment number - observe
+              that this is somewhat important because the first top segment is
+              treated differently from the other segment.
+            */
             for (const auto& segment_pair : segments)
                 segments_list.push_back( std::move(segment_pair.second) );
 
+            std::sort( segments_list.begin(), segments_list.end(),[](const Segment& seg1, const Segment& seg2) { return seg1.segmentNumber() < seg2.segmentNumber(); } );
             auto comp_pressure_drop = WellSegments::CompPressureDrop::HFA;
             std::shared_ptr<Opm::WellSegments> well_segments = std::make_shared<Opm::WellSegments>(comp_pressure_drop, segments_list);
             well.updateSegments( std::move(well_segments) );
diff --git a/tests/test_AggregateMSWData.cpp b/tests/test_AggregateMSWData.cpp
index 6501ad2d4..b6e958d6e 100644
--- a/tests/test_AggregateMSWData.cpp
+++ b/tests/test_AggregateMSWData.cpp
@@ -845,7 +845,7 @@ BOOST_AUTO_TEST_CASE(MSW_RST) {
                                  );
     const auto& iseg = amswd.getISeg();
     const auto& rseg = amswd.getRSeg();
-    auto segment = Opm::RestartIO::RstSegment(simCase.es.getUnits(), iseg.data(), rseg.data());
+    auto segment = Opm::RestartIO::RstSegment(simCase.es.getUnits(), 1, iseg.data(), rseg.data());
 }