diff --git a/lib/valueflow.cpp b/lib/valueflow.cpp
index 6b1c75101dd..e9246920e4a 100644
--- a/lib/valueflow.cpp
+++ b/lib/valueflow.cpp
@@ -2996,7 +2996,7 @@ struct ValueFlowAnalyzer : Analyzer {
             return isThisModified(tok);
 
         // bailout: global non-const variables
-        if (isGlobal() && !dependsOnThis() && Token::Match(tok, "%name% (") &&
+        if (isGlobal() && !dependsOnThis() && Token::Match(tok, "%name% (") && !tok->variable() &&
             !Token::simpleMatch(tok->linkAt(1), ") {")) {
             return isGlobalModified(tok);
         }
@@ -5938,7 +5938,7 @@ static void valueFlowForwardAssign(Token* const tok,
     }
 
     // Static variable initialisation?
-    if (vars.size() == 1 && vars.front()->isStatic() && init)
+    if (vars.size() == 1 && vars.front()->isStatic() && !vars.front()->isConst() && init)
         lowerToPossible(values);
 
     // is volatile
@@ -6057,13 +6057,25 @@ static std::list<ValueFlow::Value> truncateValues(std::list<ValueFlow::Value> va
 
 static bool isVariableInit(const Token *tok)
 {
-    return (tok->str() == "(" || tok->str() == "{") &&
-           (tok->isBinaryOp() || (tok->astOperand1() && tok->link() == tok->next())) &&
-           tok->astOperand1()->variable() &&
-           tok->astOperand1()->variable()->nameToken() == tok->astOperand1() &&
-           tok->astOperand1()->variable()->valueType() &&
-           tok->astOperand1()->variable()->valueType()->type >= ValueType::Type::VOID &&
-           !Token::simpleMatch(tok->astOperand2(), ",");
+    if (!tok)
+        return false;
+    if (!Token::Match(tok->previous(), "%var% (|{"))
+        return false;
+    if (!tok->isBinaryOp() && !(tok->astOperand1() && tok->link() == tok->next()))
+        return false;
+    if (Token::simpleMatch(tok->astOperand2(), ","))
+        return false;
+    const Variable* var = tok->astOperand1()->variable();
+    if (!var)
+        return false;
+    if (var->nameToken() != tok->astOperand1())
+        return false;
+    const ValueType* vt = var->valueType();
+    if (!vt)
+        return false;
+    if (vt->type < ValueType::Type::VOID)
+        return false;
+    return true;
 }
 
 // Return true if two associative containers intersect
diff --git a/test/testvalueflow.cpp b/test/testvalueflow.cpp
index 3e05232d251..5943a63f6cc 100644
--- a/test/testvalueflow.cpp
+++ b/test/testvalueflow.cpp
@@ -2818,6 +2818,27 @@ class TestValueFlow : public TestFixture {
                "}\n";
         ASSERT_EQUALS(true, testValueOfX(code, 4U, 3));
         ASSERT_EQUALS(false, testValueOfXKnown(code, 4U, 3));
+
+        code = "void f() {\n"
+               "    constexpr int x(123);\n"
+               "    constexpr int y(x*x);\n"
+               "    return x;\n"
+               "}";
+        ASSERT_EQUALS(true, testValueOfXKnown(code, 4U, 123));
+
+        code = "void f() {\n"
+               "    static const int x(123);\n"
+               "    static const int y(x*x);\n"
+               "    return x;\n"
+               "}";
+        ASSERT_EQUALS(true, testValueOfXKnown(code, 4U, 123));
+
+        code = "void f() {\n"
+               "    static int x(123);\n"
+               "    static int y(x*x);\n"
+               "    return x;\n"
+               "}";
+        ASSERT_EQUALS(true, testValueOfX(code, 4U, 123));
     }
 
     void valueFlowAfterSwap()