diff --git a/lib/sourcemap.js b/lib/sourcemap.js
index f2a6c8720..65c1ba7d4 100644
--- a/lib/sourcemap.js
+++ b/lib/sourcemap.js
@@ -74,12 +74,21 @@ function SourceMap(options) {
     }
 
     function add(source, gen_line, gen_col, orig_line, orig_col, name) {
+        var generatedPos = { line: gen_line + options.dest_line_diff, column: gen_col };
         if (orig_map) {
             var info = orig_map.originalPositionFor({
                 line: orig_line,
                 column: orig_col
             });
             if (info.source === null) {
+                if (generatedPos.column !== 0) {
+                    generator.addMapping({
+                        generated: generatedPos,
+                        original: null,
+                        source: null,
+                        name: null
+                    });
+                }
                 return;
             }
             source = info.source;
@@ -88,7 +97,7 @@ function SourceMap(options) {
             name = info.name || name;
         }
         generator.addMapping({
-            generated : { line: gen_line + options.dest_line_diff, column: gen_col },
+            generated : generatedPos,
             original  : { line: orig_line + options.orig_line_diff, column: orig_col },
             source    : source,
             name      : name
diff --git a/test/mocha/input-sourcemaps.js b/test/mocha/input-sourcemaps.js
index bda6e1a21..a0aa57dcf 100644
--- a/test/mocha/input-sourcemaps.js
+++ b/test/mocha/input-sourcemaps.js
@@ -1,6 +1,7 @@
 var Uglify = require('../../');
 var assert = require("assert");
 var SourceMapConsumer = require("source-map").SourceMapConsumer;
+var SourceMapGenerator = require("source-map").SourceMapGenerator;
 
 describe("input sourcemaps", function() {
     var transpilemap, map;
@@ -63,4 +64,47 @@ describe("input sourcemaps", function() {
             assert.ok(pos.line <= 2, msg);
         })
     });
+
+    it("Should preserve unmapped segments in output source map", function() {
+        var generator = new SourceMapGenerator();
+
+        generator.addMapping({
+            source: "source.ts",
+            generated: {line: 1, column: 0},
+            original: {line: 1, column: 0},
+        });
+
+        generator.addMapping({
+            source: null,
+            original: null,
+            generated: {line: 1, column: 38}
+        });
+
+        generator.addMapping({
+            source: "source.ts",
+            generated: {line: 1, column: 51},
+            original: {line: 2, column: 0},
+        });
+
+        // Everything except the "say('hello');" part is mapped to "source.ts". The "say"
+        // function call is not mapped to any original source location. e.g. this can
+        // happen when a code transformer inserts generated code in between existing code.
+        var inputFile = "function say(msg) {console.log(msg)};say('hello');process.exit(1);";
+        var result = Uglify.minify(inputFile, {
+            sourceMap: {
+                content: JSON.parse(generator.toString())
+            }
+        });
+
+        var transformedMap = new SourceMapConsumer(result.map);
+        var hasMappedSource = true;
+
+        for (let i = 0; i < result.code.length; i++) {
+            var info = transformedMap.originalPositionFor({line: 1, column: i});
+            hasMappedSource = hasMappedSource && !!info.source;
+        }
+
+        assert.equal(hasMappedSource, false, "Expected transformed source map to preserve the " +
+            "mapping without original source location");
+    });
 });