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
@@ -246,6 +246,8 @@
 // accelerate function lookup.  At that point, we should switch the depth to
 // CompileUnit, and look in these tables.
 
+#include "lldb/Symbol/CompileUnit.h"
+
 Searcher::CallbackReturn
 BreakpointResolverName::SearchCallback(SearchFilter &filter,
                                        SymbolContext &context, Address *addr) {
@@ -260,6 +262,8 @@
   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;
@@ -305,8 +309,26 @@
       SymbolContext sc;
       func_list.GetContextAtIndex(idx, sc);
       if (filter_by_cu) {
-        if (!sc.comp_unit || !filter.CompUnitPasses(*sc.comp_unit))
-          remove_it = true;
+        if (!filter_by_function) {
+          if (!sc.comp_unit || !filter.CompUnitPasses(*sc.comp_unit))
+            remove_it = true;
+        } else {
+          // TODO(kwk): Currently this appears somewhat like a hack because only
+          // the SearchFilterByModuleListAndCUOrSupportFile search filter
+          // requires eSymbolContextCompUnit and eSymbolContextFunction
+          // (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) {
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
@@ -715,9 +715,13 @@
   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); 
+  if (m_cu_spec_list.FindFileIndex(0, cu_spec, false) != UINT32_MAX)
+    return true;
+  // ^ If the primary source file associated with the symbol's compile unit is in
+  // the list of CU's or support files, that's enough.
+  // TODO(kwk): Is that enough?
+
+  return SearchFilterByModuleList::ModulePasses(sym_ctx.module_sp);
 }
 
 bool SearchFilterByModuleListAndCU::CompUnitPasses(FileSpec &fileSpec) {
@@ -811,7 +815,7 @@
 }
 
 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 inlined_42() { 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 +1,7 @@
+#include "search-support-files.h"
+#include "search-support-files2.h"
+
+int main(int argc, char *argv[]) {
+  int a = inlined_42();
+  return return_zero() + a;
+}
diff --git a/lldb/test/Shell/Breakpoint/Inputs/search-support-files2.h b/lldb/test/Shell/Breakpoint/Inputs/search-support-files2.h
new file mode 100644
--- /dev/null
+++ b/lldb/test/Shell/Breakpoint/Inputs/search-support-files2.h
@@ -0,0 +1 @@
+int return_zero() { return 0; }
\ No newline at end of file
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 +1,51 @@
+# 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: mkdir -p %t
+# RUN: cd %t
+# RUN: %build %p/Inputs/search-support-files.cpp -o dummy.out
+# RUN: %lldb -b -s %s dummy.out | FileCheck --color --dump-input=fail %s 
+
+#-------------------------------------------------------------------------------
+# Set breakpoint by function name.
+
+breakpoint set -n inlined_42
+# CHECK: (lldb) breakpoint set -n inlined_42
+# CHECK-NEXT: Breakpoint 1: where = dummy.out`inlined_42() + 4 at search-support-files.h:1:20, address = 0x0{{.*}}
+
+breakpoint set -n main
+# CHECK: (lldb) breakpoint set -n main
+# CHECK-NEXT: Breakpoint 2: where = dummy.out`main + 22 at search-support-files.cpp:5:11, address = 0x0{{.*}}
+
+#-------------------------------------------------------------------------------
+# Set breakpoint by function name and filename (the one in which the function is
+# inlined, aka the compilation unit).
+
+breakpoint set -n inlined_42 -f search-support-files.cpp
+# CHECK: (lldb) breakpoint set -n inlined_42 -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 now
+#       search by source files that are themselves no compulation units.
+
+breakpoint set -n inlined_42 -f search-support-files.h
+# CHECK: (lldb) breakpoint set -n inlined_42 -f search-support-files.h
+# CHECK-NEXT: Breakpoint 4: where = dummy.out`inlined_42() + 4 at search-support-files.h:1:20, address = 0x0{{.*}}
+
+#-------------------------------------------------------------------------------
+# 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 file that doesn't exist, we should get no results.
+
+breakpoint set -n inlined_42 -f file-not-existing.h
+# CHECK: (lldb) breakpoint set -n inlined_42 -f file-not-existing.h
+# CHECK-NEXT: Breakpoint 5: no locations (pending).
+# CHECK-NEXT: WARNING: Unable to resolve breakpoint to any actual locations.