diff --git a/include/mp/flat/redef/conic/cones.h b/include/mp/flat/redef/conic/cones.h
index 3b540e41f..d3a211769 100644
--- a/include/mp/flat/redef/conic/cones.h
+++ b/include/mp/flat/redef/conic/cones.h
@@ -141,10 +141,10 @@ class ConicConverter : public MCKeeper<MCType> {
            && (MC().NumQC2SOCPAttempted() > MC().NumQC2SOCPSucceeded()
                || MC().HasQPObjective()))       // and quadratics left in
           ||                // Some QC -> SOCP but not all
-          (((MC().NumQC2SOCPAttempted() > MC().NumQC2SOCPSucceeded()
-             && !MC().IfConvertSOCP2QC())       // and not decided to convert
+          ((MC().NumQC2SOCPAttempted() > MC().NumQC2SOCPSucceeded()
             || MC().HasQPObjective())           // or a quadratic obj
-           && MC().NumQC2SOCPSucceeded())       // Warn only if some succeeded
+           && MC().NumQC2SOCPSucceeded()        // Warn only if some succeeded
+           && !MC().IfConvertSOCP2QC())         // and not decided to convert
           ) {
         MC().AddWarning("Mix QC+cones",
                         "Not all quadratic constraints could "
diff --git a/include/mp/flat/redef/conic/qcones2qc.h b/include/mp/flat/redef/conic/qcones2qc.h
index bbd4a07b5..5a0375a5a 100644
--- a/include/mp/flat/redef/conic/qcones2qc.h
+++ b/include/mp/flat/redef/conic/qcones2qc.h
@@ -35,9 +35,18 @@ class QConeConverter :
     for (auto& coef: c)
       coef *= coef;
     c[0] = -c[0];
-    GetMC().NarrowVarBounds(x[0], 0.0, GetMC().Infty());
-    auto qc {QuadConLE{ {{}, {c, x, x}}, {0.0} }};
-    GetMC().AddConstraint(std::move(qc));
+    if (!GetMC().is_fixed(x[0])) {
+      GetMC().NarrowVarBounds(x[0], 0.0, GetMC().Infty());
+      auto qc {QuadConLE{ {{}, {c, x, x}}, {0.0} }};
+      GetMC().AddConstraint(std::move(qc));
+    } else {     // produce fixed RHS, better for Mosek
+      auto rhs = -c[0] * GetMC().fixed_value(x[0]);
+      c.erase(c.begin());
+      auto x0 = x;
+      x0.erase(x0.begin());
+      auto qc {QuadConLE{ {{}, {c, x0, x0}}, {rhs} }};
+      GetMC().AddConstraint(std::move(qc));
+    }
   }
 
   /// Reuse the stored ModelConverter
diff --git a/test/end2end/cases/categorized/fast/conic/modellist.json b/test/end2end/cases/categorized/fast/conic/modellist.json
index 1d73b5536..d7d32288f 100644
--- a/test/end2end/cases/categorized/fast/conic/modellist.json
+++ b/test/end2end/cases/categorized/fast/conic/modellist.json
@@ -61,6 +61,14 @@
       "x": 3651.48
     }
   },
+  {
+    "name" : "socp_10_qpobj",
+    "tags" : ["quadratic"],
+    "objective" : 0.0,
+    "values": {
+      "solve_result_num": 0
+    }
+  },
   {
     "name" : "expcones_01__plain",
     "objective" : 0.7821882953,
diff --git a/test/end2end/cases/categorized/fast/conic/socp_10_qpobj.mod b/test/end2end/cases/categorized/fast/conic/socp_10_qpobj.mod
new file mode 100644
index 000000000..adf3674c5
--- /dev/null
+++ b/test/end2end/cases/categorized/fast/conic/socp_10_qpobj.mod
@@ -0,0 +1,6 @@
+# From #229.
+# This is actually convex quadratic, not conic.
+
+var x {1..7} >= 0;
+minimize qobj: sum {j in 1..7} x[j]^2;
+subj to qconstr: sum {j in 1..7} x[j]^2 <= 1000;