diff --git a/lldb/source/Breakpoint/BreakpointResolverName.cpp b/lldb/source/Breakpoint/BreakpointResolverName.cpp
--- a/lldb/source/Breakpoint/BreakpointResolverName.cpp
+++ b/lldb/source/Breakpoint/BreakpointResolverName.cpp
@@ -260,6 +260,8 @@
   SymbolContextList func_list;
   bool filter_by_cu =
       (filter.GetFilterRequiredItems() & eSymbolContextCompUnit) != 0;
+  bool filter_by_function =
+      (filter.GetFilterRequiredItems() & eSymbolContextFunction) != 0;
   bool filter_by_language = (m_language != eLanguageTypeUnknown);
   const bool include_symbols = !filter_by_cu;
   const bool include_inlines = true;
@@ -304,11 +306,23 @@
       bool remove_it = false;
       SymbolContext sc;
       func_list.GetContextAtIndex(idx, sc);
-      if (filter_by_cu) {
+      if (filter_by_cu && !filter_by_function) {
         if (!sc.comp_unit || !filter.CompUnitPasses(*sc.comp_unit))
           remove_it = true;
       }
 
+      if (filter_by_cu && filter_by_function) {
+        // Keep this symbol context if it is a function call to a function
+        // whose declaration is located in a file that passes. This is needed
+        // for inlined functions (e.g. when LTO is enabled) and templates.
+        if (Type *type = sc.function->GetType()) {
+          Declaration &decl = const_cast<Declaration &>(type->GetDeclaration());
+          FileSpec &source_file = decl.GetFile();
+          if (!filter.CompUnitPasses(source_file))
+            remove_it = true;
+        }
+      }
+
       if (filter_by_language) {
         LanguageType sym_language = sc.GetLanguage();
         if ((Language::GetPrimaryLanguage(sym_language) !=
diff --git a/lldb/source/Core/SearchFilter.cpp b/lldb/source/Core/SearchFilter.cpp
--- a/lldb/source/Core/SearchFilter.cpp
+++ b/lldb/source/Core/SearchFilter.cpp
@@ -712,12 +712,7 @@
     if (m_cu_spec_list.GetSize() != 0)
       return false; // Has no comp_unit so can't pass the file check.
   }
-  FileSpec cu_spec;
-  if (sym_ctx.comp_unit)
-    cu_spec = sym_ctx.comp_unit->GetPrimaryFile();
-  if (m_cu_spec_list.FindFileIndex(0, cu_spec, false) == UINT32_MAX)
-    return false; // Fails the file check
-  return SearchFilterByModuleList::ModulePasses(sym_ctx.module_sp); 
+  return SearchFilterByModuleList::ModulePasses(sym_ctx.module_sp);
 }
 
 bool SearchFilterByModuleListAndCU::CompUnitPasses(FileSpec &fileSpec) {
@@ -811,7 +806,7 @@
 }
 
 uint32_t SearchFilterByModuleListAndCU::GetFilterRequiredItems() {
-  return eSymbolContextModule | eSymbolContextCompUnit;
+  return eSymbolContextModule | eSymbolContextCompUnit | eSymbolContextFunction;
 }
 
 void SearchFilterByModuleListAndCU::Dump(Stream *s) const {}
diff --git a/lldb/test/Shell/Breakpoint/Inputs/search-support-files.h b/lldb/test/Shell/Breakpoint/Inputs/search-support-files.h
new file mode 100644
--- /dev/null
+++ b/lldb/test/Shell/Breakpoint/Inputs/search-support-files.h
@@ -0,0 +1 @@
+int function_in_header() { return 42; }
diff --git a/lldb/test/Shell/Breakpoint/Inputs/search-support-files.cpp b/lldb/test/Shell/Breakpoint/Inputs/search-support-files.cpp
new file mode 100644
--- /dev/null
+++ b/lldb/test/Shell/Breakpoint/Inputs/search-support-files.cpp
@@ -0,0 +1,6 @@
+#include "search-support-files.h"
+
+int main(int argc, char *argv[]) {
+  int a = function_in_header();
+  return a;
+}
diff --git a/lldb/test/Shell/Breakpoint/search-support-files.test b/lldb/test/Shell/Breakpoint/search-support-files.test
new file mode 100644
--- /dev/null
+++ b/lldb/test/Shell/Breakpoint/search-support-files.test
@@ -0,0 +1,46 @@
+# In these tests we will set breakpoints on a function by name. That function
+# is defined in a header file (search-support-files.h) and will therefore be
+# inlined into the file that includes it (search-support-files.cpp).
+#
+# TODO(kwk): Check that we can also do the same with C++ methods in files?
+#            (See https://lldb.llvm.org/use/tutorial.html and look for --method.)
+
+# RUN: %build %p/Inputs/search-support-files.cpp -o %t.out
+# RUN: %lldb -b -s %s %t.out | FileCheck --color --dump-input=fail %s 
+
+#    Set breakpoint by function name.
+
+breakpoint set -n function_in_header
+# CHECK: (lldb) breakpoint set -n function_in_header
+# CHECK-NEXT: Breakpoint 1: where = {{.*}}.out`function_in_header(){{.*}} at search-support-files.h
+
+breakpoint set -n main
+# CHECK: (lldb) breakpoint set -n main
+# CHECK-NEXT: Breakpoint 2: where = {{.*}}.out`main{{.*}} at search-support-files.cpp
+
+#   Set breakpoint by function name and filename (the one in which the function
+#   is inlined, aka the compilation unit).
+
+breakpoint set -n function_in_header -f search-support-files.cpp
+# CHECK: (lldb) breakpoint set -n function_in_header -f search-support-files.cpp
+# CHECK-NEXT: Breakpoint 3: no locations (pending).
+
+#   Set breakpoint by function name and source filename (the file in which the
+#   function is defined).
+#
+#   NOTE: This test is the really interesting one as it shows that we can
+#         search by source files that are themselves no compilation units.
+
+breakpoint set -n function_in_header -f search-support-files.h
+# CHECK: (lldb) breakpoint set -n function_in_header -f search-support-files.h
+# CHECK-NEXT: Breakpoint 4: where = {{.*}}.out`function_in_header(){{.*}} at search-support-files.h
+
+#   Set breakpoint by function name and source filename. This time the file
+#   doesn't exist to prove that we haven't widen the search space too much. When
+#   we search for a function in a file that doesn't exist, we should get no
+#   results.
+
+breakpoint set -n function_in_header -f file-not-existing.h
+# CHECK: (lldb) breakpoint set -n function_in_header -f file-not-existing.h
+# CHECK-NEXT: Breakpoint 5: no locations (pending).
+# CHECK-NEXT: WARNING: Unable to resolve breakpoint to any actual locations.