diff --git a/src/climatebenchpress/compressor/compressors/utils.py b/src/climatebenchpress/compressor/compressors/utils.py
index bee70dc..efc149b 100644
--- a/src/climatebenchpress/compressor/compressors/utils.py
+++ b/src/climatebenchpress/compressor/compressors/utils.py
@@ -12,6 +12,12 @@
     np.dtype("float16"): 10,
 }
 
+NONMANTISSA_BITS = {
+    np.dtype("float32"): 32 - MANTISSA_BITS[np.dtype("float32")],
+    np.dtype("float64"): 64 - MANTISSA_BITS[np.dtype("float64")],
+    np.dtype("float16"): 16 - MANTISSA_BITS[np.dtype("float16")],
+}
+
 
 def compute_keepbits(dtype: np.dtype, rel_error: float) -> int:
     """
diff --git a/src/climatebenchpress/compressor/compressors/zfp.py b/src/climatebenchpress/compressor/compressors/zfp.py
index 9e28cb8..7ef5ef9 100644
--- a/src/climatebenchpress/compressor/compressors/zfp.py
+++ b/src/climatebenchpress/compressor/compressors/zfp.py
@@ -3,22 +3,37 @@
 import numcodecs_wasm_zfp_classic
 
 from .abc import Compressor
+from .utils import NONMANTISSA_BITS, compute_keepbits
+
+# From: https://github.com/LLNL/zfp/blob/4baa4c7eeae8e0b6a7ace4dde242ac165bcd59d9/include/zfp.h#L18
+ZFP_MIN_BITS = 1
+ZFP_MAX_BITS = 16658
 
 
 class Zfp(Compressor):
     name = "zfp"
     description = "ZFP"
 
+    @staticmethod
+    def abs_bound_codec(error_bound, **kwargs):
+        return numcodecs_wasm_zfp_classic.ZfpClassic(
+            mode="fixed-accuracy", tolerance=error_bound
+        )
+
     # NOTE:
     # ZFP mechanism for strictly supporting relative error bounds is to
-    # truncate the floating point bit representation and then use ZFP's lossless
-    # mode for compression. This is essentially equivalent to the BitRound
-    # compressors we are already implementing (with a difference what the lossless
-    # compression algorithm is).
+    # apply bitshaving and then use ZFP's lossless mode for compression.
     # See https://zfp.readthedocs.io/en/release1.0.1/faq.html#q-relerr for more details.
-
     @staticmethod
-    def abs_bound_codec(error_bound, **kwargs):
+    def rel_bound_codec(error_bound, *, dtype=None, **kwargs):
+        assert dtype is not None, "dtype must be provided"
+
+        mantissa_keepbits = compute_keepbits(dtype, error_bound)
+        total_keepbits = mantissa_keepbits + NONMANTISSA_BITS[dtype]
         return numcodecs_wasm_zfp_classic.ZfpClassic(
-            mode="fixed-accuracy", tolerance=error_bound
+            mode="expert",
+            min_bits=ZFP_MIN_BITS,
+            max_bits=ZFP_MAX_BITS,
+            max_prec=total_keepbits,
+            min_exp=-1075,
         )
diff --git a/src/climatebenchpress/compressor/compressors/zfp_round.py b/src/climatebenchpress/compressor/compressors/zfp_round.py
index bc55e81..df0f877 100644
--- a/src/climatebenchpress/compressor/compressors/zfp_round.py
+++ b/src/climatebenchpress/compressor/compressors/zfp_round.py
@@ -3,20 +3,32 @@
 import numcodecs_wasm_zfp
 
 from .abc import Compressor
+from .utils import NONMANTISSA_BITS, compute_keepbits
+from .zfp import ZFP_MAX_BITS, ZFP_MIN_BITS
 
 
 class ZfpRound(Compressor):
     name = "zfp-round"
     description = "ZFP-ROUND"
 
+    @staticmethod
+    def abs_bound_codec(error_bound, **kwargs):
+        return numcodecs_wasm_zfp.Zfp(mode="fixed-accuracy", tolerance=error_bound)
+
     # NOTE:
     # ZFP mechanism for strictly supporting relative error bounds is to
-    # truncate the floating point bit representation and then use ZFP's lossless
-    # mode for compression. This is essentially equivalent to the BitRound
-    # compressors we are already implementing (with a difference what the lossless
-    # compression algorithm is).
+    # apply bitshaving and then use ZFP's lossless mode for compression.
     # See https://zfp.readthedocs.io/en/release1.0.1/faq.html#q-relerr for more details.
-
     @staticmethod
-    def abs_bound_codec(error_bound, **kwargs):
-        return numcodecs_wasm_zfp.Zfp(mode="fixed-accuracy", tolerance=error_bound)
+    def rel_bound_codec(error_bound, *, dtype=None, **kwargs):
+        assert dtype is not None, "dtype must be provided"
+
+        mantissa_keepbits = compute_keepbits(dtype, error_bound)
+        total_keepbits = mantissa_keepbits + NONMANTISSA_BITS[dtype]
+        return numcodecs_wasm_zfp.Zfp(
+            mode="expert",
+            min_bits=ZFP_MIN_BITS,
+            max_bits=ZFP_MAX_BITS,
+            max_prec=total_keepbits,
+            min_exp=-1075,
+        )