Index: lib/Transforms/IPO/FunctionImport.cpp
===================================================================
--- lib/Transforms/IPO/FunctionImport.cpp
+++ lib/Transforms/IPO/FunctionImport.cpp
@@ -36,6 +36,13 @@
     "import-instr-limit", cl::init(100), cl::Hidden, cl::value_desc("N"),
     cl::desc("Only import functions with less than N instructions"));
 
+static cl::opt<float>
+    ImportInstrFactor("import-instr-evolution-factor", cl::init(0.7),
+                      cl::Hidden, cl::value_desc("x"),
+                      cl::desc("As we import functions, multiply the "
+                               "`import-instr-limit` threshold by this factor "
+                               "before processing newly imported functions"));
+
 // Load lazily a module from \p FileName in \p Context.
 static std::unique_ptr<Module> loadFile(const std::string &FileName,
                                         LLVMContext &Context) {
@@ -94,10 +101,11 @@
 /// Walk through the instructions in \p F looking for external
 /// calls not already in the \p CalledFunctions set. If any are
 /// found they are added to the \p Worklist for importing.
-static void findExternalCalls(const Module &DestModule, Function &F,
-                              const FunctionInfoIndex &Index,
-                              StringSet<> &CalledFunctions,
-                              SmallVector<StringRef, 64> &Worklist) {
+static void
+findExternalCalls(const Module &DestModule, Function &F,
+                  const FunctionInfoIndex &Index, StringSet<> &CalledFunctions,
+                  unsigned Threshold,
+                  SmallVectorImpl<std::pair<StringRef, unsigned>> &Worklist) {
   // We need to suffix internal function calls imported from other modules,
   // prepare the suffix ahead of time.
   std::string Suffix;
@@ -143,7 +151,7 @@
           }
         }
 
-        Worklist.push_back(It.first->getKey());
+        Worklist.push_back(std::make_pair(It.first->getKey(), Threshold));
         DEBUG(dbgs() << DestModule.getModuleIdentifier()
                      << ": Adding callee for : " << ImportedName << " : "
                      << F.getName() << "\n");
@@ -160,15 +168,18 @@
 //
 // \p ModuleToFunctionsToImportMap is filled with the set of Function to import
 // per Module.
-static void GetImportList(Module &DestModule,
-                          SmallVector<StringRef, 64> &Worklist,
-                          StringSet<> &CalledFunctions,
-                          std::map<StringRef, DenseSet<const GlobalValue *>>
-                              &ModuleToFunctionsToImportMap,
-                          const FunctionInfoIndex &Index,
-                          ModuleLazyLoaderCache &ModuleLoaderCache) {
+static void
+GetImportList(Module &DestModule,
+              SmallVectorImpl<std::pair<StringRef, unsigned>> &Worklist,
+              StringSet<> &CalledFunctions,
+              std::map<StringRef, DenseSet<const GlobalValue *>> &
+                  ModuleToFunctionsToImportMap,
+              const FunctionInfoIndex &Index,
+              ModuleLazyLoaderCache &ModuleLoaderCache) {
   while (!Worklist.empty()) {
-    auto CalledFunctionName = Worklist.pop_back_val();
+    StringRef CalledFunctionName;
+    unsigned Threshold;
+    std::tie(CalledFunctionName, Threshold) = Worklist.pop_back_val();
     DEBUG(dbgs() << DestModule.getModuleIdentifier() << ": Process import for "
                  << CalledFunctionName << "\n");
 
@@ -194,10 +205,10 @@
       llvm_unreachable("Missing summary");
     }
 
-    if (Summary->instCount() > ImportInstrLimit) {
+    if (Summary->instCount() > Threshold) {
       DEBUG(dbgs() << DestModule.getModuleIdentifier() << ": Skip import of "
                    << CalledFunctionName << " with " << Summary->instCount()
-                   << " instructions (limit " << ImportInstrLimit << ")\n");
+                   << " instructions (limit " << Threshold << ")\n");
       continue;
     }
 
@@ -253,8 +264,11 @@
     Entry.insert(F);
 
     // Process the newly imported functions and add callees to the worklist.
+    // Adjust the threshold
+    Threshold = Threshold * ImportInstrFactor;
     F->materialize();
-    findExternalCalls(DestModule, *F, Index, CalledFunctions, Worklist);
+    findExternalCalls(DestModule, *F, Index, CalledFunctions, Threshold,
+                      Worklist);
   }
 }
 
@@ -268,13 +282,15 @@
                << DestModule.getModuleIdentifier() << "\n");
   unsigned ImportedCount = 0;
 
-  /// First step is collecting the called external functions.
+  // First step is collecting the called external functions.
+  // We keep the function name as long as the import threshold for its callees.
   StringSet<> CalledFunctions;
-  SmallVector<StringRef, 64> Worklist;
+  SmallVector<std::pair<StringRef, unsigned>, 64> Worklist;
   for (auto &F : DestModule) {
     if (F.isDeclaration() || F.hasFnAttribute(Attribute::OptimizeNone))
       continue;
-    findExternalCalls(DestModule, F, Index, CalledFunctions, Worklist);
+    findExternalCalls(DestModule, F, Index, CalledFunctions, ImportInstrLimit,
+                      Worklist);
   }
   if (Worklist.empty())
     return false;
Index: test/Transforms/FunctionImport/adjustable_threshold.ll
===================================================================
--- /dev/null
+++ test/Transforms/FunctionImport/adjustable_threshold.ll
@@ -0,0 +1,23 @@
+; Do setup work for all below tests: generate bitcode and combined index
+; RUN: llvm-as -function-summary %s -o %t.bc
+; RUN: llvm-as -function-summary %p/Inputs/funcimport.ll -o %t2.bc
+; RUN: llvm-lto -thinlto -o %t3 %t.bc %t2.bc
+
+; Test import with default progressive instruction factor
+; RUN: opt -function-import -summary-file %t3.thinlto.bc %s -import-instr-limit=10 -S | FileCheck %s --check-prefix=CHECK --check-prefix=INSTLIM-DEFAULT
+; INSTLIM-DEFAULT: call void @globalfunc2()
+
+; Test import with a reduced progressive instruction factor
+; RUN: opt -function-import -summary-file %t3.thinlto.bc %s -import-instr-limit=10 -import-instr-evolution-factor=0.5 -S | FileCheck %s --check-prefix=CHECK --check-prefix=INSTLIM-PROGRESSIVE
+; INSTLIM-PROGRESSIVE-NOT: call void @globalfunc2()
+
+
+
+declare void @globalfunc1()
+
+define void @entry() {
+entry:
+  call void @globalfunc1()
+  ret void
+}
+