diff --git a/src/plugins/clangcodemodel/clangmodelmanagersupport.cpp b/src/plugins/clangcodemodel/clangmodelmanagersupport.cpp
index 679e41004bf..b92f12279f3 100644
--- a/src/plugins/clangcodemodel/clangmodelmanagersupport.cpp
+++ b/src/plugins/clangcodemodel/clangmodelmanagersupport.cpp
@@ -517,12 +517,14 @@ void ClangModelManagerSupport::updateLanguageClient(ProjectExplorer::Project *pr
                         && currentClient->project() == docProject) {
                     continue;
                 }
-                if (!docProject || docProject == project) {
-                    if (currentClient)
-                        currentClient->closeDocument(doc);
-                    LanguageClientManager::openDocumentWithClient(doc, client);
-                    hasDocuments = true;
+                if (docProject != project
+                        && (docProject || !ProjectFile::isHeader(doc->filePath()))) {
+                    continue;
                 }
+                if (currentClient)
+                    currentClient->closeDocument(doc);
+                LanguageClientManager::openDocumentWithClient(doc, client);
+                hasDocuments = true;
             }
 
             for (auto it = m_queuedShadowDocuments.begin(); it != m_queuedShadowDocuments.end();) {
@@ -625,11 +627,13 @@ void ClangModelManagerSupport::claimNonProjectSources(ClangdClient *client)
         }
         if (!ClangdSettings::instance().sizeIsOkay(doc->filePath()))
             continue;
-        if (!ProjectExplorer::SessionManager::projectForFile(doc->filePath())) {
-            if (currentClient)
-                currentClient->closeDocument(doc);
-            LanguageClientManager::openDocumentWithClient(doc, client);
-        }
+        if (ProjectExplorer::SessionManager::projectForFile(doc->filePath()))
+            continue;
+        if (client->project() && !ProjectFile::isHeader(doc->filePath()))
+            continue;
+        if (currentClient)
+            currentClient->closeDocument(doc);
+        LanguageClientManager::openDocumentWithClient(doc, client);
     }
 }
 
@@ -717,7 +721,7 @@ void ClangModelManagerSupport::onEditorOpened(Core::IEditor *editor)
             return;
         if (sessionModeEnabled())
             project = nullptr;
-        else if (!project)
+        else if (!project && ProjectFile::isHeader(document->filePath()))
             project = fallbackProject();
         if (ClangdClient * const client = clientForProject(project))
             LanguageClientManager::openDocumentWithClient(textDocument, client);
diff --git a/src/plugins/cppeditor/cppprojectfile.cpp b/src/plugins/cppeditor/cppprojectfile.cpp
index c28f41a2291..c5a5d57d5b8 100644
--- a/src/plugins/cppeditor/cppprojectfile.cpp
+++ b/src/plugins/cppeditor/cppprojectfile.cpp
@@ -6,6 +6,7 @@
 #include "cppeditorconstants.h"
 
 #include <coreplugin/icore.h>
+#include <utils/filepath.h>
 #include <utils/mimeutils.h>
 
 #include <QDebug>
@@ -125,6 +126,11 @@ bool ProjectFile::isHeader(ProjectFile::Kind kind)
     }
 }
 
+bool ProjectFile::isHeader(const Utils::FilePath &fp)
+{
+    return isHeader(classify(fp.toString()));
+}
+
 bool ProjectFile::isSource(ProjectFile::Kind kind)
 {
     switch (kind) {
diff --git a/src/plugins/cppeditor/cppprojectfile.h b/src/plugins/cppeditor/cppprojectfile.h
index 71310fec8a2..16894555cf5 100644
--- a/src/plugins/cppeditor/cppprojectfile.h
+++ b/src/plugins/cppeditor/cppprojectfile.h
@@ -7,6 +7,8 @@
 
 #include <QString>
 
+namespace Utils { class FilePath; }
+
 namespace CppEditor {
 
 class CPPEDITOR_EXPORT ProjectFile
@@ -39,6 +41,7 @@ public:
 
     static bool isSource(Kind kind);
     static bool isHeader(Kind kind);
+    static bool isHeader(const Utils::FilePath &fp);
     static bool isC(Kind kind);
     static bool isCxx(Kind kind);
     static bool isAmbiguousHeader(const QString &filePath);