diff --git a/benchmark/matobj/bench-submat.g b/benchmark/matobj/bench-submat.g
index 0b10bf85b2..b5ee2697de 100644
--- a/benchmark/matobj/bench-submat.g
+++ b/benchmark/matobj/bench-submat.g
@@ -7,13 +7,15 @@ TestExtractingSubmatrix := function(m)
     rows := [2..NrRows(m)-2];
     cols := [3..NrCols(m)-1];
 
-    PrintHeadline("m{}{}");
-    MyBench(function()
-        local u, x;
-        for u in [1..QuoInt(100000,NrRows(m)*NrCols(m))] do
-            x:=m{rows}{cols};
-        od;
-    end);
+    if not IsPlistMatrixRep(m) then
+        PrintHeadline("m{}{}");
+        MyBench(function()
+            local u, x;
+            for u in [1..QuoInt(100000,NrRows(m)*NrCols(m))] do
+                x:=m{rows}{cols};
+            od;
+        end);
+    fi;
 
     PrintHeadline("ExtractSubMatrix");
     MyBench(function()
@@ -32,13 +34,15 @@ TestCopyingSubmatrix := function(m)
     rows := [2..NrRows(m)-2];
     cols := [3..NrCols(m)-1];
 
-    PrintHeadline("m{}{}:=n{}{}");
-    MyBench(function()
-        local u;
-        for u in [1..QuoInt(100000,NrRows(m)*NrCols(m))] do
-            x{rows}{cols}:=m{rows}{cols};
-        od;
-    end);
+    if not IsPlistMatrixRep(m) then
+        PrintHeadline("m{}{}:=n{}{}");
+        MyBench(function()
+            local u;
+            for u in [1..QuoInt(100000,NrRows(m)*NrCols(m))] do
+                x{rows}{cols}:=m{rows}{cols};
+            od;
+        end);
+    fi;
 
     PrintHeadline("CopySubMatrix");
     MyBench(function()
@@ -62,18 +66,21 @@ for dim in [10, 100] do
     PrintBoxed(Concatenation("Now testing in dimension ", String(dim)));
 
     m:=IdentityMat(dim);;
-    RunMatTest("integer matrix", m);
+    RunMatTest("integer matrix: list of lists", m);
+
+    m:=IdentityMatrix(Integers, dim);;
+    RunMatTest("integer matrix: IsPlistMatrixRep", m);
 
     m:=IdentityMat(dim,GF(2));;
     RunMatTest("GF(2) rowlist", m);
 
-    m:=IdentityMat(dim,GF(2));; ConvertToMatrixRep(m);;
+    m:=IdentityMatrix(GF(2), dim);;
     RunMatTest("GF(2) compressed matrix", m);
 
     m:=IdentityMat(dim,GF(7));;
     RunMatTest("GF(7) rowlist", m);
 
-    m:=IdentityMat(dim,GF(7));; ConvertToMatrixRep(m);;
+    m:=IdentityMatrix(GF(8), dim);;
     RunMatTest("GF(7) compressed matrix", m);
 
 # TODO: also add cvec matrices
diff --git a/benchmark/matobj/bench-subvec.g b/benchmark/matobj/bench-subvec.g
new file mode 100644
index 0000000000..8e2ede2ea9
--- /dev/null
+++ b/benchmark/matobj/bench-subvec.g
@@ -0,0 +1,81 @@
+ReadGapRoot("benchmark/matobj/bench.g");
+
+
+TestExtractingSubvector := function(v)
+    local cols;
+
+    cols := [3..Length(v)-1];
+
+    if not IsPlistVectorRep(v) then
+        PrintHeadline("v{}");
+        MyBench(function()
+            local u, x;
+            for u in [1..QuoInt(100000, Length(v))] do
+                x := v{cols};
+            od;
+        end);
+    fi;
+
+    PrintHeadline("ExtractSubVector");
+    MyBench(function()
+        local u, x;
+        for u in [1..QuoInt(100000, Length(v))] do
+            x := ExtractSubVector(v, cols);
+        od;
+    end);
+end;
+
+TestCopyingSubvector := function(v)
+    local x, cols;
+
+    x := ShallowCopy(v);
+    cols := [3..Length(v)-1];
+
+    if not IsPlistVectorRep(v) then
+        PrintHeadline("x{}:=v{}");
+        MyBench(function()
+            local u;
+            for u in [1..QuoInt(100000, Length(v))] do
+                x{cols} := v{cols};
+            od;
+        end);
+    fi;
+
+    PrintHeadline("CopySubVector");
+    MyBench(function()
+        local u;
+        for u in [1..QuoInt(100000, Length(v))] do
+            CopySubVector(v, x, cols, cols);
+        od;
+    end);
+end;
+
+RunVecTest := function(desc, v)
+    Print("\n");
+    PrintBoxed(Concatenation("Testing subvector extraction for ", desc));
+    TestExtractingSubvector(v);
+    Print(TextAttr.2, "...now testing subvector copying...\n", TextAttr.reset);
+    TestCopyingSubvector(v);
+end;
+
+for dim in [10, 100] do
+    PrintBoxed(Concatenation("Now testing in dimension ", String(dim)));
+
+    v := [1..dim] * 0;;
+    RunVecTest("integer vector: plain list", v);
+
+    v := Vector(IsPlistVectorRep, Integers, [1..dim]);;
+    RunVecTest("integer vector: IsPlistVectorRep", v);
+
+    v := [1..dim] * One(GF(2));;
+    RunVecTest("GF(2) row vector", v);
+
+    v := NewVector(IsGF2VectorRep, GF(2), [1..dim] * One(GF(2)));;
+    RunVecTest("GF(2) compressed vector", v);
+
+    v := [1..dim] * One(GF(7));;
+    RunVecTest("GF(7) row vector", v);
+
+    v := NewVector(Is8BitVectorRep, GF(7), [1..dim] * One(GF(7)));;
+    RunVecTest("GF(7) 8-bit vector", v);
+od;
diff --git a/lib/matobj.gi b/lib/matobj.gi
index 652dddccad..35ae1ccbe0 100644
--- a/lib/matobj.gi
+++ b/lib/matobj.gi
@@ -749,9 +749,9 @@ InstallMethod( \{\},
     return Vector( Unpack( v ){ poss }, v );
     end );
 
-InstallMethod( ExtractSubVector,
-    "generic method for a vector object and a list",
-    [ IsVectorObj, IsList ],
+InstallOtherMethod( ExtractSubVector,
+    "generic method for a row vector or vector object and a list",
+    [ IsRowVectorOrVectorObj, IsList ],
     { v, l } -> v{ l } );
 
 InstallMethod( ExtractSubMatrix,
@@ -759,20 +759,10 @@ InstallMethod( ExtractSubMatrix,
     [ IsMatrixObj, IsList, IsList ],
     { M, rowpos, colpos } -> Matrix( Unpack( M ){ rowpos }{ colpos }, M ) );
 
-# Hack from recog package
-InstallOtherMethod( ExtractSubMatrix, "hack: for lists of compressed vectors",
-[ IsList, IsList, IsList ],
-function( m, poss1, poss2 )
-  local i,n;
-  n := [];
-  for i in poss1 do
-      Add(n,ShallowCopy(m[i]{poss2}));
-  od;
-  if IsFFE(m[1,1]) then
-      ConvertToMatrixRep(n);
-  fi;
-  return n;
-end );
+InstallOtherMethod( ExtractSubMatrix,
+    "generic method for a matrix and two lists",
+    [ IsMatrix, IsList, IsList ],
+    { M, rowpos, colpos } -> M{ rowpos }{ colpos } );
 
 InstallMethod( CopySubVector,
     "generic method for row vectors and vector objects",
@@ -788,6 +778,13 @@ InstallMethod( CopySubVector,
     od;
 end );
 
+InstallMethod( CopySubVector,
+    "generic method for row vectors",
+  [ IsRowVector, IsRowVector and IsMutable, IsList, IsList ],
+  function(src, dst, scols, dcols)
+    dst{dcols} := src{scols};
+end );
+
 
 #############################################################################
 ##
diff --git a/lib/matobj2.gd b/lib/matobj2.gd
index c7cd9f0c4a..21f4af9a32 100644
--- a/lib/matobj2.gd
+++ b/lib/matobj2.gd
@@ -434,7 +434,8 @@ DeclareGlobalFunction( "ConcatenationOfVectors" );
 ##  </ManSection>
 ##  <#/GAPDoc>
 ##
-DeclareOperation( "ExtractSubVector", [ IsVectorObj, IsList ] );
+DeclareOperationKernel( "ExtractSubVector",
+    [ IsRowVectorOrVectorObj, IsList ], EXTRACT_SUB_VECTOR );
 
 
 #############################################################################
@@ -896,9 +897,9 @@ DeclareOperation( "Randomize", [ IsRandomSource, IsMatrixOrMatrixObj and IsMutab
 ##  </ManSection>
 ##  <#/GAPDoc>
 ##
-DeclareOperation( "CopySubVector",
+DeclareOperationKernel( "CopySubVector",
     [ IsRowVectorOrVectorObj, IsRowVectorOrVectorObj and IsMutable,
-      IsList, IsList ] );
+      IsList, IsList ], COPY_SUB_VECTOR );
 
 
 #############################################################################
@@ -956,7 +957,8 @@ DeclareOperation( "DistanceOfVectors", [ IsVectorObj, IsVectorObj ] );
 ##  </ManSection>
 ##  <#/GAPDoc>
 ##
-DeclareOperation( "ExtractSubMatrix", [ IsMatrixOrMatrixObj, IsList, IsList ] );
+DeclareOperationKernel( "ExtractSubMatrix",
+    [ IsMatrixOrMatrixObj, IsList, IsList ], EXTRACT_SUB_MATRIX );
 
 
 #############################################################################
@@ -1005,8 +1007,11 @@ DeclareOperation( "MutableCopyMatrix", [ IsMatrixOrMatrixObj ] );
 ##  </ManSection>
 ##  <#/GAPDoc>
 ##
-DeclareOperation( "CopySubMatrix",
-    [ IsMatrixOrMatrixObj, IsMatrixOrMatrixObj, IsList, IsList, IsList, IsList ] );
+DeclareOperationKernel( "CopySubMatrix",
+    [ IsMatrixOrMatrixObj, IsMatrixOrMatrixObj, IsList, IsList, IsList, IsList ],
+    COPY_SUB_MATRIX );
+#T We intentionally keep the second argument declaration broad, mirroring
+#T the pre-existing operation declaration for compatibility with packages.
 
 
 #############################################################################
diff --git a/src/lists.c b/src/lists.c
index dc329b0966..feb5c1584c 100644
--- a/src/lists.c
+++ b/src/lists.c
@@ -1611,6 +1611,99 @@ void            AsssListLevel (
 }
 
 
+/****************************************************************************
+**
+*F  FuncEXTRACT_SUB_VECTOR( <self>, <vec>, <poss> ) . . `EXTRACT_SUB_VECTOR'
+*/
+static Obj ExtractSubVectorOper;
+
+static Obj FuncEXTRACT_SUB_VECTOR(Obj self, Obj vec, Obj poss)
+{
+    if (IS_PLIST(vec)) {
+        CheckIsPossList("List Elements", poss);
+        return ELMS_LIST(vec, poss);
+    }
+
+    return DoOperation2Args(ExtractSubVectorOper, vec, poss);
+}
+
+
+/****************************************************************************
+**
+*F  FuncCOPY_SUB_VECTOR( <self>, <src>, <dst>, <scols>, <dcols> )
+*/
+static Obj CopySubVectorOper;
+
+static Obj FuncCOPY_SUB_VECTOR(
+    Obj self, Obj src, Obj dst, Obj scols, Obj dcols)
+{
+    if (IS_PLIST(src) && IS_PLIST(dst)) {
+        Obj rhss;
+
+        CheckIsPossList("List Assignments", scols);
+        CheckIsPossList("List Assignments", dcols);
+        rhss = ELMS_LIST(src, scols);
+        AsssListCheck(dst, dcols, rhss);
+        return 0;
+    }
+
+    return DoOperation4Args(CopySubVectorOper, src, dst, scols, dcols);
+}
+
+
+/****************************************************************************
+**
+*F  FuncEXTRACT_SUB_MATRIX( <self>, <mat>, <rows>, <cols> )
+*/
+static Obj ExtractSubMatrixOper;
+
+static Obj FuncEXTRACT_SUB_MATRIX(Obj self, Obj mat, Obj rows, Obj cols)
+{
+    if (IS_PLIST(mat)) {
+        Obj submat;
+
+        CheckIsPossList("List Elements", rows);
+        CheckIsPossList("List Elements", cols);
+        submat = ELMS_LIST(mat, rows);
+        ElmsListLevel(submat, cols, 1);
+        return submat;
+    }
+
+    return DoOperation3Args(ExtractSubMatrixOper, mat, rows, cols);
+}
+
+
+/****************************************************************************
+**
+*F  FuncCOPY_SUB_MATRIX( <self>, <src>, <dst>, <srows>, <drows>, <scols>,
+*F  <dcols> )
+*/
+static Obj CopySubMatrixOper;
+
+static Obj FuncCOPY_SUB_MATRIX(
+    Obj self, Obj src, Obj dst, Obj srows, Obj drows, Obj scols, Obj dcols)
+{
+    if (IS_PLIST(src) && IS_PLIST(dst)) {
+        Obj srcsub;
+        Obj dstsub;
+
+        CheckIsPossList("List Assignments", srows);
+        CheckIsPossList("List Assignments", drows);
+        CheckIsPossList("List Assignments", scols);
+        CheckIsPossList("List Assignments", dcols);
+
+        srcsub = ELMS_LIST(src, srows);
+        ElmsListLevel(srcsub, scols, 1);
+        dstsub = ELMS_LIST(dst, drows);
+        AsssListLevel(dstsub, dcols, srcsub, 1);
+        return 0;
+    }
+
+    return DoOperation6Args(CopySubMatrixOper, src, dst, srows, drows, scols,
+                            dcols);
+}
+
+
 /****************************************************************************
 **
 *F  PLAIN_LIST(<list>)  . . . . . . . . . . .  convert a list to a plain list
@@ -1953,6 +2046,13 @@ static StructGVarOper GVarOpers[] = {
 
     GVAR_OPER_4ARGS(ASS_MAT, mat, row, col, obj, &AssMatOper),
     GVAR_OPER_3ARGS(ELM_MAT, mat, row, col, &ElmMatOper),
+    GVAR_OPER_2ARGS(EXTRACT_SUB_VECTOR, vec, poss, &ExtractSubVectorOper),
+    GVAR_OPER_4ARGS(COPY_SUB_VECTOR, src, dst, scols, dcols,
+                    &CopySubVectorOper),
+    GVAR_OPER_3ARGS(EXTRACT_SUB_MATRIX, mat, rows, cols,
+                    &ExtractSubMatrixOper),
+    GVAR_OPER_6ARGS(COPY_SUB_MATRIX, src, dst, srows, drows, scols, dcols,
+                    &CopySubMatrixOper),
 
     GVAR_OPER_3ARGS(SWAP_MAT_ROWS, mat, row1, row2, &SwapMatRows),
     GVAR_OPER_3ARGS(SWAP_MAT_COLS, mat, col1, col2, &SwapMatCols),
diff --git a/tst/testinstall/MatrixObj/CopySubVector.tst b/tst/testinstall/MatrixObj/CopySubVector.tst
index 5c702e6089..33cea42c90 100644
--- a/tst/testinstall/MatrixObj/CopySubVector.tst
+++ b/tst/testinstall/MatrixObj/CopySubVector.tst
@@ -79,7 +79,8 @@ gap> l4;
 
 #
 gap> CopySubVector( l1, l3, [1,2], [1] );
-Error, source and destination index lists must be of equal length
+Error, List Assignments: <rhss> must have the same length as <poss> (lengths a\
+re 2 and 1)
 
 #
 gap> STOP_TEST("CopySubVector.tst");
diff --git a/tst/testinstall/MatrixObj/ExtractSubMatrix.tst b/tst/testinstall/MatrixObj/ExtractSubMatrix.tst
new file mode 100644
index 0000000000..35517c5f25
--- /dev/null
+++ b/tst/testinstall/MatrixObj/ExtractSubMatrix.tst
@@ -0,0 +1,13 @@
+gap> START_TEST("ExtractSubMatrix.tst");
+gap> IsBoundGlobal("EXTRACT_SUB_MATRIX");
+true
+gap> EXTRACT_SUB_MATRIX = ExtractSubMatrix;
+true
+gap> m1 := [ [ 1, 2, 3 ], [ 4, 5, 6 ] ];
+[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
+gap> ExtractSubMatrix( m1, [ 2, 1 ], [ 3, 1 ] );
+[ [ 6, 4 ], [ 3, 1 ] ]
+gap> m2 := IdentityMatrix( Integers, 4 );;
+gap> Unpack( ExtractSubMatrix( m2, [ 2, 4 ], [ 4, 2 ] ) );
+[ [ 0, 1 ], [ 1, 0 ] ]
+gap> STOP_TEST("ExtractSubMatrix.tst");
diff --git a/tst/testinstall/MatrixObj/ExtractSubvector.tst b/tst/testinstall/MatrixObj/ExtractSubvector.tst
index 42af85ac22..81224516ab 100644
--- a/tst/testinstall/MatrixObj/ExtractSubvector.tst
+++ b/tst/testinstall/MatrixObj/ExtractSubvector.tst
@@ -1,6 +1,8 @@
 gap> START_TEST("ExtractSubVector.tst");
 gap> l1 := [1,2,3,4,5,6];
 [ 1, 2, 3, 4, 5, 6 ]
+gap> ExtractSubVector( l1, [1,2,4] );
+[ 1, 2, 4 ]
 gap> v3 := Vector(GF(5), l1*One(GF(5)));
 [ Z(5)^0, Z(5), Z(5)^3, Z(5)^2, 0*Z(5), Z(5)^0 ]
 gap> ExtractSubVector( v3, [1,2,4] );