diff --git a/src/cmd/compile/internal/ssa/compile.go b/src/cmd/compile/internal/ssa/compile.go
index b3c7544ad12..d8b0b0a5c1d 100644
--- a/src/cmd/compile/internal/ssa/compile.go
+++ b/src/cmd/compile/internal/ssa/compile.go
@@ -270,6 +270,7 @@ var passes = [...]pass{
 	{name: "checkLower", fn: checkLower, required: true},
 	{name: "late phielim", fn: phielim},
 	{name: "late copyelim", fn: copyelim},
+	{name: "phi tighten", fn: phiTighten},
 	{name: "late deadcode", fn: deadcode},
 	{name: "critical", fn: critical, required: true}, // remove critical edges
 	{name: "likelyadjust", fn: likelyadjust},
diff --git a/src/cmd/compile/internal/ssa/tighten.go b/src/cmd/compile/internal/ssa/tighten.go
index ecb43c101d2..2f7c30929d7 100644
--- a/src/cmd/compile/internal/ssa/tighten.go
+++ b/src/cmd/compile/internal/ssa/tighten.go
@@ -86,3 +86,26 @@ func tighten(f *Func) {
 		}
 	}
 }
+
+// phiTighten moves constants closer to phi users.
+// This pass avoids having lots of constants live for lots of the program.
+// See issue 16407.
+func phiTighten(f *Func) {
+	for _, b := range f.Blocks {
+		for _, v := range b.Values {
+			if v.Op != OpPhi {
+				continue
+			}
+			for i, a := range v.Args {
+				if !a.rematerializeable() {
+					continue // not a constant we can move around
+				}
+				if a.Block == b.Preds[i].b {
+					continue // already in the right place
+				}
+				// Make a copy of a, put in predecessor block.
+				v.SetArg(i, a.copyInto(b.Preds[i].b))
+			}
+		}
+	}
+}