diff --git a/src/compression.jl b/src/compression.jl
index 2492c85..4ea160a 100644
--- a/src/compression.jl
+++ b/src/compression.jl
@@ -37,7 +37,9 @@ function GzipCompressor(;level::Integer=Z_DEFAULT_COMPRESSION,
     elseif !(9 ≤ windowbits ≤ 15)
         throw(ArgumentError("windowbits must be within 9..15"))
     end
-    return GzipCompressor(ZStream(), level, windowbits+16)
+    zstream = ZStream()
+    finalizer(compress_finalizer!, zstream)
+    return GzipCompressor(zstream, level, windowbits+16)
 end
 
 const GzipCompressorStream{S} = TranscodingStream{GzipCompressor,S} where S<:IO
@@ -85,7 +87,9 @@ function ZlibCompressor(;level::Integer=Z_DEFAULT_COMPRESSION,
     elseif !(9 ≤ windowbits ≤ 15)
         throw(ArgumentError("windowbits must be within 9..15"))
     end
-    return ZlibCompressor(ZStream(), level, windowbits)
+    zstream = ZStream()
+    finalizer(compress_finalizer!, zstream)
+    return ZlibCompressor(zstream, level, windowbits)
 end
 
 const ZlibCompressorStream{S} = TranscodingStream{ZlibCompressor,S} where S<:IO
@@ -133,7 +137,9 @@ function DeflateCompressor(;level::Integer=Z_DEFAULT_COMPRESSION,
     elseif !(9 ≤ windowbits ≤ 15)
         throw(ArgumentError("windowbits must be within 9..15"))
     end
-    return DeflateCompressor(ZStream(), level, -Int(windowbits))
+    zstream = ZStream()
+    finalizer(compress_finalizer!, zstream)
+    return DeflateCompressor(zstream, level, -Int(windowbits))
 end
 
 const DeflateCompressorStream{S} = TranscodingStream{DeflateCompressor,S} where S<:IO
@@ -155,17 +161,6 @@ end
 # Methods
 # -------
 
-function TranscodingStreams.finalize(codec::CompressorCodec)
-    zstream = codec.zstream
-    if zstream.state != C_NULL
-        code = deflate_end!(zstream)
-        if code != Z_OK
-            zerror(zstream, code)
-        end
-    end
-    return
-end
-
 function TranscodingStreams.startproc(codec::CompressorCodec, state::Symbol, error_ref::Error)
     if codec.zstream.state == C_NULL
         code = deflate_init!(codec.zstream, codec.level, codec.windowbits)
diff --git a/src/decompression.jl b/src/decompression.jl
index 67bff25..65a0c9d 100644
--- a/src/decompression.jl
+++ b/src/decompression.jl
@@ -35,7 +35,9 @@ function GzipDecompressor(;windowbits::Integer=Z_DEFAULT_WINDOWBITS, gziponly::B
     if !(8 ≤ windowbits ≤ 15)
         throw(ArgumentError("windowbits must be within 8..15"))
     end
-    return GzipDecompressor(ZStream(), windowbits+(gziponly ? 16 : 32))
+    zstream = ZStream()
+    finalizer(decompress_finalizer!, zstream)
+    return GzipDecompressor(zstream, windowbits+(gziponly ? 16 : 32))
 end
 
 const GzipDecompressorStream{S} = TranscodingStream{GzipDecompressor,S} where S<:IO
@@ -78,7 +80,9 @@ function ZlibDecompressor(;windowbits::Integer=Z_DEFAULT_WINDOWBITS)
     if !(8 ≤ windowbits ≤ 15)
         throw(ArgumentError("windowbits must be within 8..15"))
     end
-    return ZlibDecompressor(ZStream(), windowbits)
+    zstream = ZStream()
+    finalizer(decompress_finalizer!, zstream)
+    return ZlibDecompressor(zstream, windowbits)
 end
 
 const ZlibDecompressorStream{S} = TranscodingStream{ZlibDecompressor,S} where S<:IO
@@ -121,7 +125,9 @@ function DeflateDecompressor(;windowbits::Integer=Z_DEFAULT_WINDOWBITS)
     if !(8 ≤ windowbits ≤ 15)
         throw(ArgumentError("windowbits must be within 8..15"))
     end
-    return DeflateDecompressor(ZStream(), -Int(windowbits))
+    zstream = ZStream()
+    finalizer(decompress_finalizer!, zstream)
+    return DeflateDecompressor(zstream, -Int(windowbits))
 end
 
 const DeflateDecompressorStream{S} = TranscodingStream{DeflateDecompressor,S} where S<:IO
@@ -143,17 +149,6 @@ end
 # Methods
 # -------
 
-function TranscodingStreams.finalize(codec::DecompressorCodec)
-    zstream = codec.zstream
-    if zstream.state != C_NULL
-        code = inflate_end!(zstream)
-        if code != Z_OK
-            zerror(zstream, code)
-        end
-    end
-    return
-end
-
 function TranscodingStreams.startproc(codec::DecompressorCodec, ::Symbol, error_ref::Error)
     # indicate that no input data is being provided for future zlib compat
     codec.zstream.next_in = C_NULL
diff --git a/src/libz.jl b/src/libz.jl
index 507b7e1..ca62fb8 100644
--- a/src/libz.jl
+++ b/src/libz.jl
@@ -23,6 +23,18 @@ mutable struct ZStream
     reserved::Culong
 end
 
+@assert typemax(Csize_t) ≥ typemax(Cuint)
+
+function zalloc(::Ptr{Cvoid}, items::Cuint, size::Cuint)::Ptr{Cvoid}
+    s, f = Base.Checked.mul_with_overflow(items, size)
+    if f
+        C_NULL
+    else
+        ccall(:jl_malloc, Ptr{Cvoid}, (Csize_t,), s%Csize_t)
+    end
+end
+zfree(::Ptr{Cvoid}, p::Ptr{Cvoid}) = ccall(:jl_free, Cvoid, (Ptr{Cvoid},), p)
+
 function ZStream()
     ZStream(
         # input
@@ -32,7 +44,9 @@ function ZStream()
         # message and state
         C_NULL, C_NULL,
         # memory allocation
-        C_NULL, C_NULL, C_NULL,
+        @cfunction(zalloc, Ptr{Cvoid}, (Ptr{Cvoid}, Cuint, Cuint)),
+        @cfunction(zfree, Cvoid, (Ptr{Cvoid}, Ptr{Cvoid})),
+        C_NULL,
         # data type, adler and reserved
         0, 0, 0)
 end
@@ -83,6 +97,11 @@ function deflate_end!(zstream::ZStream)
     return ccall((:deflateEnd, libz), Cint, (Ref{ZStream},), zstream)
 end
 
+function compress_finalizer!(zstream::ZStream)
+    deflate_end!(zstream)
+    nothing
+end
+
 function deflate!(zstream::ZStream, flush::Integer)
     return ccall((:deflate, libz), Cint, (Ref{ZStream}, Cint), zstream, flush)
 end
@@ -99,6 +118,11 @@ function inflate_end!(zstream::ZStream)
     return ccall((:inflateEnd, libz), Cint, (Ref{ZStream},), zstream)
 end
 
+function decompress_finalizer!(zstream::ZStream)
+    inflate_end!(zstream)
+    nothing
+end
+
 function inflate!(zstream::ZStream, flush::Integer)
     return ccall((:inflate, libz), Cint, (Ref{ZStream}, Cint), zstream, flush)
 end
diff --git a/test/big-mem-tests.jl b/test/big-mem-tests.jl
index a8cd1b1..e728fa9 100644
--- a/test/big-mem-tests.jl
+++ b/test/big-mem-tests.jl
@@ -6,16 +6,21 @@
 using Test
 using CodecZlib
 
-# Enable this when https://github.com/JuliaIO/CodecZlib.jl/issues/88 is fixed.
-# @testset "memory leak" begin
-#     function foo()
-#         for i in 1:1000000
-#             c = transcode(GzipCompressor(), zeros(UInt8,16))
-#             u = transcode(GzipDecompressor(), c)
-#         end
-#     end
-#     foo()
-# end
+@testset "memory leak" begin
+    function foo()
+        for (encode, decode) in [
+            (GzipCompressor, GzipDecompressor),
+            (ZlibCompressor, ZlibDecompressor),
+            (DeflateCompressor, DeflateDecompressor),
+        ]
+            for i in 1:1000000
+                c = transcode(encode(), zeros(UInt8,16))
+                u = transcode(decode(), c)
+            end
+        end
+    end
+    foo()
+end
 
 @testset "Big Memory Tests" begin
     Sys.WORD_SIZE == 64 || error("tests require 64 bit word size")