diff --git a/compression/sfp-inl.h b/compression/sfp-inl.h
index 3be36ec..7ca877b 100644
--- a/compression/sfp-inl.h
+++ b/compression/sfp-inl.h
@@ -218,7 +218,7 @@ class SfpCodec {
 #define SFP_IF_GENERIC_DEC(D) void* yes = nullptr
 #endif
 
-  // Decodes u8 `encoded` into `lo` and `hi` bytes of bf16. 12 ops.
+  // Decodes u8 `encoded` into `lo` and `hi` bytes of bf16. 9 ops.
   template <class D, HWY_IF_U8_D(D), SFP_IF_GENERIC_DEC(D)>
   static HWY_INLINE void DecBytes(D d, hn::Vec<D> encoded, hn::Vec<D>& lo,
                                   hn::Vec<D>& hi) {
@@ -233,31 +233,27 @@ class SfpCodec {
     // Special-case zero, negated so we can use MaskedAddOr. Signed comparison
     // is fine because we have cleared the sign bit.
     const hn::Mask<D> is_nonzero = SignedGt(d, encoded, k0);
-    // If MSB is clear, we have two mantissa bits, otherwise three.
+    // If bit 6 is clear, we have two mantissa bits, otherwise three.
     const hn::Mask<D> is_small_e = SignedLt(d, encoded, hn::Set(d, 64));
-    // If is_small_e, add/left-shift 0xxxx.mm to 0xxxx.mm0; else keep 1xxx.mmm.
-    const hn::Vec<D> e4m3 =
-        hn::MaskedAddOr(encoded, is_small_e, encoded, encoded);
-    HWY_DASSERT(hn::AllTrue(d, hn::Lt(e4m3, k80)));
-    const hn::Vec<D> e = hn::ShiftRight<3>(e4m3);  // 4-bit exponent only
-    HWY_DASSERT(hn::AllTrue(d, hn::Lt(e, Set(d, 16u))));
-    // The encoded exponent for 2^0 is 15, so subtract 15. Add 127 for the
-    // binary32/bf16 bias. Subtract another 8 if is_small_e because its lowest
-    // encoded value (0) should be less than the lowest 'large' exponent 2^-7.
-    const hn::Vec<D> e_bias = hn::IfThenElse(
-        is_small_e, hn::Set(d, 127u - 15u - 8u), hn::Set(d, 127u - 15u));
-    // Special-case zero or add e_bias. If encoded=0, e and e4m3 are zero, but
-    // we must zero e_bias to get the desired all-zero bf16.
-    const hn::Vec<D> biased_e = hn::MaskedAddOr(k0, is_nonzero, e_bias, e);
-    // The decoded binary32 exponent should be at most 2^0.
-    HWY_DASSERT(hn::AllTrue(d, hn::Lt(biased_e, k80)));
+    // For encoded in [1, 8), hi = 0x34; encoded = 0x40 => hi = 0x3C including
+    // (encoded >> 4) == 4, so add 0x38.
+    const hn::Vec<D> e_bias =
+        hn::IfThenElse(is_small_e, hn::Set(d, 0x34), hn::Set(d, 0x38));
 
-    // Shift the MSB of e4m3's mantissa into the MSB of the bf16 mantissa.
-    const hn::Vec<D> m7 = hn::ShiftLeft<4>(e4m3);
-    // Lower byte of bf16 = exponent LSB || mantissa.
-    lo = hn::BitwiseIfThenElse(k80, hn::ShiftLeft<7>(biased_e), m7);
-    // Upper byte of bf16 = sign || lower 7 bits of exponent.
-    hi = hn::BitwiseIfThenElse(k80, sign_in_msb, hn::ShiftRight<1>(biased_e));
+    // The low byte of bf16 is encoded << (is_small_e ? 5 : 4).
+    const hn::Vec<D> shl1_if_small =
+        hn::MaskedAddOr(encoded, is_small_e, encoded, encoded);
+    lo = hn::ShiftLeft<4>(shl1_if_small);
+    // Lower 4 bits always zero.
+    HWY_DASSERT(hn::AllTrue(d, hn::Eq(hn::And(lo, Set(d, 15u)), hn::Zero(d))));
+
+    // The upper byte of bf16 is e_bias + (encoded >> (is_small_e ? 3 : 4)).
+    const hn::Vec<D> shr_3_or_4 = hn::ShiftRight<4>(shl1_if_small);
+    // .. except when encoded=0: hi = 0, and lo is already 0.
+    const hn::Vec<D> e7 = hn::MaskedAddOr(k0, is_nonzero, e_bias, shr_3_or_4);
+    HWY_DASSERT(hn::AllTrue(d, hn::Lt(e7, Set(d, 64u))));  // <= 0x3F
+    // .. also insert the sign bit.
+    hi = hn::BitwiseIfThenElse(k80, sign_in_msb, e7);
   }
 
   // Encodes `num` bf16 values from `in_bf` to `out_packed`. Their magnitude
diff --git a/compression/sfp_test.cc b/compression/sfp_test.cc
index 150df56..68f3e14 100644
--- a/compression/sfp_test.cc
+++ b/compression/sfp_test.cc
@@ -101,6 +101,29 @@ void TestAllUnique() {
   }
 }
 
+// For deriving the new shift-based decoder, which is 3 ops faster than the
+// previous "assemble from binary32 bits" method.
+void TestAllFastDecode() {
+  for (size_t sfp = 0; sfp < 128; ++sfp) {
+    const float f = F32FromSFP8(sfp);
+    const uint32_t u = hwy::BitCastScalar<uint32_t>(f);
+    const uint32_t lo = (u >> 16) & 0xFF;
+    const uint32_t hi = u >> 24;
+    const bool is_small = sfp < 0x40;
+    const uint32_t base = is_small ? 0x34 : 0x38;
+    const uint32_t fast_lo = (sfp << (is_small ? 5 : 4)) & 0xFF;
+    uint32_t fast_hi = base + (sfp >> (is_small ? 3 : 4));
+    if (sfp == 0) fast_hi = 0;
+
+    // fprintf(stderr, "sfp %2zx -> %6.3E %x %x\n", sfp, f, lo, hi);
+    if (fast_lo != lo || fast_hi != hi) {
+      HWY_ABORT(
+          "mismatch sfp %2zx -> %6.3E lo %2x fastLo %2x hi %2x fastHi %2x\n",
+          sfp, f, lo, fast_lo, hi, fast_hi);
+    }
+  }
+}
+
 // ------------------------------ Foreach compressed representation
 
 // Encode
@@ -550,6 +573,7 @@ namespace gcpp {
 HWY_BEFORE_TEST(SfpTest);
 HWY_EXPORT_AND_TEST_P(SfpTest, PrintTables);
 HWY_EXPORT_AND_TEST_P(SfpTest, TestAllUnique);
+HWY_EXPORT_AND_TEST_P(SfpTest, TestAllFastDecode);
 HWY_EXPORT_AND_TEST_P(SfpTest, TestAllDecEnc);
 HWY_EXPORT_AND_TEST_P(SfpTest, TestAllGolden);
 HWY_EXPORT_AND_TEST_P(SfpTest, TestAllEncDec);